5. On the swamp, there are 64 bumps, they are arranged in an $8 \times 8$ square. On each bump sits a frog or a toad. Frogs never lie, while toads only tell lies. Each of them, both frogs and toads, croaked: “At least one of the neighboring bumps has a toad.” What is the maximum number of toads that could sit on these bumps?

Neighboring bumps are those located horizontally and vertically in the rows of the square, diagonal bumps are not considered neighbors.
Solution. Note that frogs cannot sit on adjacent lily pads, otherwise they would be telling the truth. If we divide the lily pads into pairs, there will be no more than one frog in each pair, otherwise they would be telling the truth. Therefore, there can be no more than 32 frogs, as the lily pads can be divided into 32 pairs. Let's provide an example of how 32 frogs can be seated. We will color the 64 lily pads in a chessboard pattern with two colors. If we place the frogs on the black lily pads and the toads on the white ones, the condition of the problem will be satisfied.

Answer: 32