5. Given a $2021 \times 2021$ grid. 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 $3 \times 5$ and $5 \times 3$ rectangle contains a chip, wins. Petya starts. Which player can guarantee a win regardless of the opponent's actions?
Answer: Petya

Solution. Petya should move in such a way that Vasya cannot win on the next move. We will show that he can always achieve this. If there is a pair of non-intersecting empty rectangles $3 \times 5$ on the board, Petya should place a chip so that they remain even after his move. If such a move is impossible, then there are only two non-intersecting empty rectangles $3 \times 5$ left on the board, and all other cells are occupied by chips. Therefore, $2021^{2}$ - 30 chips have been placed on the board. This is an odd number, and thus it is Vasya's turn. If any two empty rectangles $3 \times 5$ intersect, there will be a cell common to all squares. Then Petya will place a chip in this cell and win.