To simplify the given expression, we can use the trigonometric identity:

cos(2x) = 1 - 2sin^2(x)

Substitute cos(2x) with the identity:

(1 - 2sin^2(x)) + 5sin(x)cos(x) + 5cos^2(x) = 0

Expand:

1 - 2sin^2(x) + 5sin(x)cos(x) + 5cos^2(x) = 0

Rearrange:

5cos^2(x) - 2sin^2(x) + 5sin(x)cos(x) + 1 = 0

Now we have the simplified expression.