Is it possible for divide by 4 or 5 programmable frequency divider to have different max operating frequency? If yes what might possible cause it to happen? Thanks.
Sure. A divide by 4 can be just 2 flip flop circuits in series.
A divide by 5 circuit needs 3 flip flops, and some way to reset them to zero when the count reaches 5. That extra circuitry has propagation delay, and if the frequency gets high enough, starts to reset unreliably.