1) I had a meeting with five of our students.
2) I had meetings with five of our students.
Could these sentences be used if I had one meeting with each of the five?
It seems to me that '2' is a very general statement and could be used almost in any case. It could be even used if, say, I had three meetings in all. Once with one and the other times with two students.
Neither of them suggests five separate meetings, each with one person. #1 suggests one meeting with six people in total in attendance. #2 is even less specific.
If you had one meeting with each student, you had five meetings in total. So you can say "I had five meetings, each with a different student".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.