What is the minimum bandwidth required for a digital communication system using 32-QAM modulation?
QAM really has nothing to do with PSK at all. It's just two channels of ASK that are combined together using two subcarriers that have a fixed phase shift between them.

To prevent ISI in an ASK signal, you need to be able to transmit at a minimum the main "lobe" of the power spectrum with linear phase shift. The lobe is defined by the first nulls in the PSD, which occur at &plusmn; the symbol rate/2, for a total bandwidth that's equal to the symbol rate.

So, yes, you're on the right track: The bandwidth in Hz is equal to the symbol rate, which is equal to the bitrate divided by the number of bits per symbol, or 5.