The bank lends an amount at 7%. The individual immediately pays the full amount into someone else's bank account. If the bank needs cash (which it probably doesn't on a day to day basis because most of its depositors leave money where it is) it can borrow that amount from the other bank at 5.5% and profit from the margin. So the amounts are eventually consistent.
That's the basic logic: modern banking adds in a central bank that guarantees that it will lend enough to solvent banks at 5.5% to meet their customers' withdrawal requirements even if everyone pulls money out, banks treating each others' credit as equivalent in value to cash because they can always convert it, and a bunch of rules about lending needing to be banked with bank capital and other weighted assets to keep lending growth from being silly.
That's the basic logic: modern banking adds in a central bank that guarantees that it will lend enough to solvent banks at 5.5% to meet their customers' withdrawal requirements even if everyone pulls money out, banks treating each others' credit as equivalent in value to cash because they can always convert it, and a bunch of rules about lending needing to be banked with bank capital and other weighted assets to keep lending growth from being silly.