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I know the two properties of convolution that are related to my question
But my question is, how can I use those two to calculate $$ y(t)=x(5t)*\delta(t-5) $$
Set $f(t)=x(5t)$ and use your rule number 2: $$f(t)\star \delta(t-t_0)=f(t-t_0)=\ldots$$
Required, but never shown