To solve the equation cos(3x + π) = cos(5x), we can use the identity cos(a) = cos(b) if and only if a = ±b + 2πn, where n is an integer.

In this case, we have 3x + π = ±5x + 2πn.

For the positive case, we have 3x + π = 5x + 2πn.
Rearranging the equation, we get 2x = π - 2πn.
Dividing both sides by 2, we have x = (π - 2πn)/2.
Simplifying further, we get x = π/2 - πn.

For the negative case, we have 3x + π = -5x + 2πn.
Rearranging the equation, we get 8x = -π + 2πn.
Dividing both sides by 8, we have x = (-π + 2πn)/8.
Simplifying further, we get x = -π/8 + πn/4.

Therefore, the solutions to the equation cos(3x + π) = cos(5x) are:
x = π/2 - πn, where n is an integer, and
x = -π/8 + πn/4, where n is an integer.