Find the value of x.

The two given equations are vertical angles, which mean they are the same.
Set the two equations to equal and solve for x:
13x-23 = 5x+17
Add 23 to each side:
13x = 5x+40
Subtract 5x from each side:
8x = 40
Divide both sides by 8:
x = 40/8
x = 5