To solve the equation 2cos^3x = sin(5π/2 - x), we will use trigonometric identities.

First, let's rewrite the equation using sine and cosine:

2cos^3x = cos(π/2 - (5π/2 - x))

Now, using the trigonometric identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we can rewrite the right side of the equation:

2cos^3x = cos(π/2)cos(5π/2 - x) + sin(π/2)sin(5π/2 - x)

Now, let's simplify the right side of the equation:

2cos^3x = 0 + 1*sin(5π/2 - x)

2cos^3x = sin(5π/2 - x)

Since both sides of the equation are equal, the equation is true. Therefore, the solution to the equation 2cos^3x = sin(5π/2 - x) is x can be any real number.