To decimate a 5 MHz sampled signal to a sampling rate of 10 Hz properly we need to define the expected passband and the performance needed over that passband in terms of passband distortion and dynamic range or signal to noise ratio that needs to be maintained. We also need to know the noise floor or spectral characteristics of the 5 MHz signal from DC to 2.5 MHz (this may be the quantization noise given by the number of bits used, or there may be additional signal occupying that spectrum).
Once defined, we can then design the decimation filter, which is an anti-alias filter required prior to down-sampling. This filter can be either an IIR or an FIR, but in my experience once actual performance is considered the FIR can be accomplished with less resources and less challenges related to precision issues especially for fixed point implementations.
Consider that the ideal decimation filter is to pass with minimum distortion the passband from DC to some upper limit $f_b$ that is less than Nyquist (Nyquist here is at 5 Hz), and suppress the alias bands which will begin at 10 Hz - $f_b$. I doubt any significant rejection of this first alias can be achieved with a single tap IIR running at 5 MHz unless we have no concern for the passband shape, and then all the additional alias bands that will be at $10N \pm f_b$ Hz throughout the rest of the original spectrum (with $N$ as positive integers). Even if we don't have a known interference in these alias regions, such a decimation filterwill have significant SNR degradation due to noise accumulation from the 250,000 alias's within the primary Nyquist band (at the higher 5 MHz rate) that will accumulate in band if not properly filtered out! ($10log_{10}(250,000) = 54$ dB or 9 bits if there was no filter).
A realizable solution is a multistage decimation since even a single stage FIR filter with such transition bandwidth requirements would be prohibitive in comparison. If actual performance requirements needed can be given, we can further detail the trade to see if there is indeed a counter example. A CIC (Cascade-Integrator-Comb) with a subsequent shaping filter could also be a very efficient solution if the passband needed is actually significantly smaller than Nyquist for the final 10 Hz rate, or alternatively CIC down to an intermediate frequency such as 100 Hz and then a higher performance decimation to go from 100 Hz to 10 Hz where the inverse Sinc shaping to compensate for the CIC could be included.
Update:
The OP added further details suggesting the desired result is the best estimate of the short term mean value. (Estimate of temperature). To determine the best filter we do need to understand the spectral characteristics of the 5 MHz sampled signal (assuming all prior details to ensure anti-aliasing of signals that may exist above ~ 10 MHz and beyond. (Related to this and not to do with the filter is ensuring that DC-offset errors which would typically be introduced in the sampling process have been properly calibrated out noting that such offset itself would typically change with temperature). However short of having this information, if we make an assumption of white noise and that the signal is stationary enough (over the averaging interval suggested by the decimated sampling rate), it is known that the optimum filter is a simple moving average under that noise condition. A CIC filter conveniently is such a moving average filter! This means if we were to decimate the waveform by a factor of 500,000, a CIC implemented as a moving average over 500,000 samples would result in the best SNR result for a signal occupying the resulting Nyquist bandwidth. Notably the resulting noise (with a white noise input) would also be white and opportunity remains to further average the result if it is determined that the signal occupies much less bandwidth and is sufficiently stationary over the considered averaging interval. Below I compare the frequency response of the OP's IIR to that for a 500,000 sample moving average filter, and below that I show what that implementation looks like as a functional block diagram.
What we see in this plot is how for the purpose of decimating to a 10 Hz rate, the suggested IIR filter is insufficient in rejecting aliases that would fold back in to degrade the estimate of the mean (DC component). These aliases would be at every integer multiple of the final output rate or 10 Hz. Notice, beautifully, how the CIC provides infinite rejection (limited in the plot due to resolution of the plot only) at each of these alias locations! Certainly this suggests for the IIR approach that a larger $\alpha$ is needed (current $2^{16}$), but even once reduced to match the general roll-off shape of the CIC, we won't get the added benefits of the nulls placed at the harmonics of the sampling rate that the CIC provides.
The implementation of this first order CIC is quite simple! As shown below, the CIC decimator to go from 5 MHz to 10 Hz consists of an accumulator, followed by down-sampling or selecting every 500,000th sample from the accumulator output, and then taking the successive difference of the resulting 10 Hz samples. The accumulator precision is such that it can only roll-over once in any 500,000 sample interval (and specifically that it does roll-over on an overflow). If a 32 bit accumulator was used, this would specify that the maximum input precision be $32-log_2(500,000)+ 1 = 14$ bits. (Such that a worst case continuous full-scale input would not overflow more than once in the 500,000 sample averaging interval.)
It would appear that the CIC is itself an IIR filter, given the feedback structure, but it in fact has a finite impulse response and is indeed an FIR filter. It is just an efficient implementation of a moving tap FIR filter (with 500,000 unity gain coefficients!), followed by a down sampler to select every 500,000th sample- the result would be identical.
As mentioned, further details are needed for the actual design- specifically the spectrum and the statistics of the signal.
For instance, if the signal was stationary (it isn't!) and the spectrum indicated all other noise is white, then the optimum filter to estimate the mean is a simple average. For non-stationary signals (such as temperature versus time) under the condition of additive white noise only, the optimum filter is a moving average constrained over time to the bias instability floor (using terms from gyroscope sensors). What is great to know is the CIC filter IS exactly a simple moving average filter as the decimator filter and commonly used in decimator implementations due to its grand simplicity! The optimum time duration (and therefore optimum decimation) is easily determined from a plot of the Allan Deviation, where the temperature measurement would be treated as a "frequency input" (the Allan Deviation is primarily used to measure the frequency stability of oscillators). The Allan Deviation provides a plot of rms error versus time duration $\tau$, and if averaging of the signal would provide any benefit, the error would decrease as $\tau$ increases, ultimately to a minimum suggesting the best averaging time.
Example ADEV plot from https://www.phidgets.com/docs/Allan_Deviation_Primer showing a minimum for their example data at around 100 seconds. This means for this particular data, the estimate of the mean would be improved by increasing the averaging time up to 100 seconds, but any longer than that and the result would not get better, and ultimately as we go longer than 200 seconds or so, the estimate would degrade. (Typically this plot is shown with the vertical axis on a log scale as well). If the ADEV is decreasing at a rate of $1/\sqrt{\tau}$, the noise in that region can be considered white. We see this on this chart with the ADEV dropping by a factor of 10 when $\tau$ goes from 0.1 to 10 (a factor of 100), and thus the noise would be white over a frequency range from approximately from at least 10 Hz to the floor at 1/100th of a Hz.
For the users application this may suggest a final sampling rate that is larger or smaller than 5 Hz. A review of the spectrum (to see if narrow band interferences need to also be filtered out) and then once removed, a review of the Allan Deviation of the resulting waveform under maximum temperature change conditions to determine the optimum $\tau$ would then lead to the best sampling rate and filter.
An additional note related to measuring the mean value at DC is the limitation that will be given due to $1/f$ noise. The review of the spectrum under condition of stable temperature would indicate if this is of concern, and if so lead to other sensing architectures that would avoid measuring DC.
