To solve this equation, we first need to simplify the left side:

(x - 12 23/40) + 5 8/15
= x - 12 23/40 + 5 8/15
= x - 492/40 + 120/15
= x - 12 12/40 + 8
= x - 12 3/40 + 8
= x - 12 3/40 + 8(40/40)
= x - 12 3/40 + 320/40
= x - (12 + 3 + 320)/40
= x - 335/40

Now we set this equal to 13 19/24 and solve for x:

x - 335/40 = 13 19/24
x - 335/40 = 13 19/24
x = 13 19/24 + 335/40
x = (1324 + 19)/24 + (335/40)
x = (312 + 19)/24 + 335/40
x = 331/24 + 335/40
x = (33140 + 33524)/(2440)
x = (13240 + 8040)/(960)
x = 21280/960
x = 22

Therefore, the solution to the equation is x = 22.