To solve the equation -5sin$2x$ - 16$sin(x)-cos(x)$ + 8 = 0, we can use trigonometric identities to simplify it.

Let's start by expanding -5sin$2x$ using the double-angle identity: sin$2x$ = 2sin$x$cos$x$.

-5sin$2x$ = -5$2sin(x)cos(x)$ = -10sin$x$cos$x$

Next, expand -16$sin(x)-cos(x)$:

-16sin$x$ + 16cos$x$

Substitute these simplified expressions back into the original equation:

-10sin$x$cos$x$ - 16sin$x$ + 16cos$x$ + 8 = 0

Now, we can rearrange the terms and factor out common factors:

-2sin$x$$5cos(x)+8$ + 16$cos(x)+5$ = 0

Now, we have factored the original equation. To solve for x, we need to set each factor to zero:

-2sin$x$ = 0 or 5cos$x$ + 8 = 0
sin$x$ = 0 cos$x$ = -8/5

The solutions for sin$x$= 0 are x = 0, π

The solutions for cos$x$ = -8/5 are no real solutions, as the cosine values are limited to $$-1,1$$

Therefore, the solutions for the original equation are x = 0, π.