The commonly called 5.1 format uses only surround channels, which are defined as rear/side channels in ITU-R BS 775. The case you want to deal with (turning rear surround channels to side surround channels) is therefore not explicitly defined.
Notice that in the referenced ITU document, the case of changing the number of rear/sides loudspeakers reproducing a common rear/side signal is mentioned (see Note 5) :
If more than two rear/side loudspeakers are used, the LS signal should
be fed to each of the side/rear loudspeakers on the left side of the
room and the RS signal should be fed to each of the side/rear
loudspeakers on the right side of the room. In doing so, it will be
necessary to reduce the signal gain such that the total power emitted
by the loudspeakers carrying the LS (or RS) signal is the same as if
that signal had been reproduced over a single loudspeaker.
In your case, as you are keeping the same number of loudspeakers, I would simply map Rear Left (resp. Rear Right) to Side Left (resp. Side Right) with a gain of 1.0.
The case is different if you want to downmix a 7.1 format (of which several mappings are mentioned in ITU-R BS 2159, see figure 20) to a 5.1 format, where you will need to take into account which mapping is used in the 7.1 format to define downmix coefficients.
Also notice that although there are commonly used coefficients when downmixing multi-channels formats, most codecs use metadata sets to allow the content creator to specify it's own coefficients in order to preserve artistic intent (see Dolby Metadata Guide, part 4 for example).