1. `player_score>=computer_score` makes computer win even when they score the same. A comparison should be `>` instead of `>=' (same for the next clause).

2. The game as coded may terminate early (before reaching 5 rounds). For me, it contradict the requirements.

3. User input shall be validated (is it really a number?) somehow.

3. I don't know if you covered functions already. If so, factor out all the copy-pastes into functions.