You can't do this algorithmically -- or I really mean to say you shouldn't. But as a musician and arranger, there are infinite possibilities to take some material and rework it into a different format.
To the specific example of "Take Five", consider the 5/4 rhythm groove:
5 | 1 2 3 4 5 |
4 | e e - e e - q q |
For me, I answer the question of "how would I play this groove in 4/4?" with the following:
4 | 1 2 3 4 |
4 | e e - e q q |
... which could easily be made to have a reggae feel.
I've left out some notes to accomplish this -- since a groove effectively is the rhythm, you can't really avoid that. But for the melody you don't have to leave out any notes at all -- the rhythms can be compressed and modified to "economize out" the missing beat.
Again, not algorithmically; putting the entire melody into 5:4 tuplets would be pretty uninspired. But you can get creative, shortening held notes and compressing rhythms, but mostly trying to retain the points of emphasis that exist in the original melody and rhythm/articulation.
A simple but good guide to this would be to try to retain the placement of beat 1 of each bar after translating. (In other words, make the note that occurs on beat 1 of every bar in 5/4 translate to the first beat of every bar in 4/4.)
As to the question of why? Well, it's fun, it's memorable (as evidenced by your jazz ensemble instructor), and of course making your ears and internal rhythmic clock do "weird" stuff can only benefit you as a musician.