I am learning about the perfect 5th and perfect 4th. When tuning a drumset, why would you choose one over the other?
First, I wouldn't normally tune to perfect fourths or perfect fifths. Instead, I would look for the lowest resonance of the shell and start off tuning to that. From there, if I don't like the sound, I might tune up to the next resonance. Finding notes where the shell resonates helps you get the most sound and character out of the drum. This is why DW shells have their fundamental notes stamped on the inside wood of the shell.
Second, if I did want to tune to specific notes regardless of the shells, I would probably go for perfect fourths (descending) over fifths. That's because descending fifths tend to create a resolution that would not sound right for most of a song. Descending fourths do create a type of resolution (aka cadence) but it's not nearly as strong as the feeling of descending perfect fifths.
Bear in mind that a P5 might be C to a higher G in actual notes, whereas a P4 might be G to a higher C. Same ideas, but inverse of each other. So you may want to start with the lowest drum pitch - big floor tom - and tune up in 4ths or fifths from there, or start with the smallest tom, and tune down in 4ths or fifths from there.
Also bear in mind that when tuned to something, they will resonate in that something key rather well, but if the band plays in another key, they may just clash quite well.
Since the snare, used with the strainer on, essentially has no pitch that will interfere with anything, just make sure the skin is balanced all round. If you use it as another 'tom', then you will probably want to pitch it to match the others. Same idea with kick - balance the skin(s), but not match it.