To solve the equation:

(tg5x - tg3x) / (1 + tg5x*tg3x) = -sqrt(3)

First, let's simplify the left-hand side of the equation by using the identity:

tan(a-b) = (tan(a) - tan(b)) / (1 + tan(a)*tan(b))

Using this identity, we can rewrite the left-hand side of the equation as:

(tan(5x) - tan(3x)) / (1 + tan(5x)*tan(3x)) = tan(5x - 3x) = tan(2x)

So, the equation becomes:

tan(2x) = -sqrt(3)

Now, we can take the arctangent of both sides of the equation to get:

2x = arctan(-sqrt(3))

We know that arctan(-sqrt(3)) = -pi/3, so:

2x = -pi/3

x = -pi/6

Therefore, the solution to the equation is x = -pi/6.