Then how do the banks profit from deposits, if they can't use them for lending?
But the 'bank deposit' itself is just an entry on the liability side of the bank's balance sheet, they can't profit from that. The bank might pay interest on it to the depositor because they want to encourage them to deposit more, because deposits coming in give the bank cheap liquidity, so stop them having to borrow reserves from other banks etc. to maintain liquidity.
I'm not saying you're wrong. It just seems like something is missing from the picture in your explanation.
When I opened my bank account, I deposited say £5000 cash. What does the bank do with this money?
I was under the impression that the bank doesn't actually keep this £5000 in cash, only £500 maybe, and uses the rest to lend money, but you seem to be saying that they can't actually use my deposit.
It burns it. Probably quite literally.
The cash represents a transfer from the central bank into the commercial bank's deposit account at the central bank - for which it receives an interest rate.
Cash is just a receipt for deposits held at the central bank.
Banks can also attract reserves by borrowing in money markets (cheap but short term) or issuing long term debt (stable but expensive), or by persuading customers to open accounts and keep them in positive balance. In practice it will use a mix of all three, attempting to match the maturity profile of its liabilities.
The central bank will also create reserves and lend them to your bank if your bank can't raise them elsewhere for some reason. But borrowing from the central bank can spook investors, and it's also expensive.
A bank that doesn't have reserves can't settle its debts to other banks (like the debt you incurred by moving your £5000) and so can't function in the banking system. It has to get reserves from somewhere, and persuading consumers to park deposits in an account is one useful way to do so.