To solve the equation, we can first combine the terms on the left side:

(x - 7/15) + 5/8 = 17/24
x - 7/15 + 5/8 = 17/24

Now, we need to find a common denominator for 15 and 8, which is 120.

x - 64/120 + 75/120 = 51/120
x + 11/120 = 51/120

Now, we can isolate x by subtracting 11/120 from both sides:

x = 51/120 - 11/120
x = 40/120
x = 1/3

So, the solution to the equation is x = 1/3.