To solve the equation:
Cos(7x) - sin(5x) = 0

We can rewrite the equation in terms of sine and cosine using the angle addition and subtraction formulas:
Cos(7x) - sin(5x) = cos(7x) - cos(π/2 - 5x)

Now we can use the cosine subtraction formula:
Cos(7x) - cos(π/2 - 5x) = 2 sin((7x + π/2 - 5x)/2) sin((7x - π/2 + 5x)/2)

Simplifying further:
Cos(7x) - sin(5x) = 2 sin((7x + π/2 - 5x)/2) sin((7x - π/2 + 5x)/2)
= 2 sin((2x + π/2)/2) sin((6x - π/2)/2)
= 2 cos(x) sin(3x - π/4)

Since the product of two terms is zero, at least one of them must be zero, thus:
cos(x) = 0 => x = π/2 + kπ , k is an integer
sin(3x - π/4) = 0
=> 3x - π/4 = mπ, m is an integer
=> x = (mπ + π/ 4) / 3

Therefore, the solution to the equation Cos(7x) - sin(5x) = 0 is:
x = π/2 + kπ or x = (mπ + π/ 4) / 3, where k and m are integers.