To evaluate this expression, we first need to convert all trigonometric functions to sine and cosine functions using the following identities:

cos(-x) = cos(x)ctg(x) = cot(x) = 1/tan(x)tg(-x) = -tan(x)

Given the expression:

3cos(-180) + 5ctg(270) - 2tg(0) - tg(-60)

We can simplify it as follows:

3cos(-180) = 3cos(180) = 3(-1) = -3
5ctg(270) = 5cot(270) = 5(0) = 0
2tg(0) = 2tan(0) = 2(0) = 0
tg(-60) = -tan(60) = -√3

Substitute back into the original expression:

-3 + 0 - 0 - (-√3) = -3 + √3

Therefore, the value of the expression is -3 + √3.