To solve the equation cos(5x) = sin(π/2), we need to use the trigonometric identity sin(π/2) = cos(0).

Therefore, the equation becomes:
cos(5x) = cos(0)

Since the cosine function is an even function, meaning cos(-θ) = cos(θ), we can simplify the equation to:
5x = 0 + 2kπ or 5x = 2π + 2kπ
where k is an integer.

Now, we solve for x by dividing by 5:
x = 0/5 + 2kπ/5 or x = 2π/5 + 2kπ/5

Therefore, the solutions for x are:
x = 0 + 2kπ/5 or x = 2π/5 + 2kπ/5
where k is an integer.