How does the fractional reserve banking system work?
The bank hasn't made £1080 out of nothing. Bob paid that money into the bank. It wasn't in the bank earlier, and it is in the bank now. Alice's account has been increased by £1000. And the bank has £80 extra that it earnt by lending to Bob.

It's helpful to distinguish the money that the bank holds, from the amount of money in the whole system, and from the amount of money the bank owns.

£1080 has left the rest of the system, and entered the bank.

The bank's own capital starts at £5000 and finishes at £5080 (ignoring any interest it's paid to Alice, and its operating costs).

Alice's account starts at £500, and finishes at £1500.

Bob's account starts and ends at £100.