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Usually student loans have a minimum amount that would be due each month, & I'm sure it's not going to be $5 or less. Probably $50 or so, unless you are on a special repayment plan or something. I don't think it's worth keeping it open. Installment accounts are a small part of your FICO, & while you *may* take a small ding for not having any open installment accounts after you close it, I wouldn't worry about it much.
Definitely read the agreement. The loan payment should be fixed and should be including both principal and interest. Paying less than the scheduled amount can result in late payments or default.