To solve this equation, we will use trigonometric identities to simplify both sides of the equation.

We know that:
sin^2 x + cos^2 x = 1

Starting with the left side of the equation:
sinx + 1 + sin5x
= sinx + sin5x + 1
= 2sin(3x)cos(2x) + 1

Now, we simplify the right side of the equation using the double angle identity for cosine:
2cos^2 x
= 2(1 - sin^2 x)
= 2 - 2sin^2 x

Substitute 2sin^2 x with 2 - 2cos^2 x in the equation:
2sin(3x)cos(2x) + 1 = 2 - 2cos^2 x

Rearranging, we get:
2sin(3x)cos(2x) = 1 - 2cos^2 x
sin(3x) = (1 - 2cos^2 x) / 2cos(2x)

This is as simplified as we can get without making approximations or giving a numerical solution.