Most of the savings accounts I've ever had have had a $5 minimum balance.

Why all the fuss about making sure I have $5 in the bank? Surely they aren't making that much more money on me when I have $5 in the bank vs. when I have $0, right?

The savings account is kind of like a loan to them. You put the money aside that you're saving up and in the meantime they get to use it to provide loans and provide you interest in return. If the account is empty they are gaining nothing from it, but still have to track it.

The bank does this to avoid people just leaving their old savings accounts with no balance on them.

Maintaining the account takes a tiny bit of work and the bank does not like that people have a lot of unused accounts that they have to keep track of. $5 is a high enough sum that people care about it and take two seconds transferring to an active account. Most banks will allow you to keep your account without any balance for some time but the $5 limit gives them an excuse to close unused accounts.

Plus $5 may not be much for one account, but if thousands of accounts were empty, that would be a big difference for their capacity to lend money.