5. Given a grid board $2020 \times 2021$. Petya and Vasya are playing the following game. They take turns placing chips in free cells of the board. The player who, after their move, ensures that every $4 \times 4$ square contains a chip wins. Petya starts. Which player can guarantee a win regardless of the opponent's actions?
Answer: Vasya

Solution. Vasya should move in such a way that Petya cannot win on his next move. We will show that he can always achieve this. If there is a pair of non-overlapping empty $4 \times 4$ squares on the board, Petya must place a chip so that they remain even after his move. If such a move is impossible, then there are only two non-overlapping empty $4 \times 4$ squares on the board, and all other cells are occupied by chips. Therefore, $2020 \cdot 2021$ - 32 chips have been placed on the board. This is an even number, so it is Petya's turn now. If any two empty $4 \times 4$ squares overlap, there will be a cell common to all squares. Then Vasya will place a chip in this cell and win.