First, we'll need to determine what sort of relationship the given angles have. We can see that the two angles make a straight line, so they must be supplementary, or a linear pair.
Supplementary angles/Linear Pairs create a straight line, as seen here, which means that the sum of the angles is 180 degrees.
Therefore, the two given expressions/angles will add up to 180.
(5x - 16) + (x + 10) = 180
6x - 6 = 180
6x = 186
x = 31
Answer: x = 31
Hope this helps!