That #5(16mm) limit was in older ACI318 versions, cannot seem to find it's equivalent in 2019 version,but it's probably in there somewhere. But I suspect that in addition to the reason kootk gave that it is simply a bar size that works ok from a detailing perspective and also provides a decent capacity to tie members together without really having to think about things. Smaller sized bars might tend to buckle for example using typical wider stirrup spacings where the top bars have not been specifically designed as compression reinforcement. More empirical based than theoretical I suspect regarding the size.
Sanira, refer to 9.7.3.8 in ACI318-19 for the development limits regarding 1/3 & 1/4 strength limits kootk noted for beams (similar limits exist for slabs as well). Theses rules of thumb are actually codified.