The interior angle measures of a triangle add up to 180°.
Make ∠A + B + C = 180.
x + (4x) + (5x - 13) = 180
Add all like terms.
10x - 13 = 180
Add 13 to both sides.
10x = 193
Divide both sides by 10.
x = 19.3
Now plug in x into m∠C, (5x - 13).
5(19.3) - 13 = 83.5
The m∠C is 83.5°.