To solve this expression, we must first convert the mixed numbers into improper fractions:

5 12 = 5 + (12/12) = 5 + 1 = 6

1 5_8 = 1 + (5/8) = 1 + 0.625 = 1.625

2 1_24 = 2 + (1/24) = 2 + 0.0416 = 2.0416

Now, we can substitute the improper fractions back into the expression:

6 - (1.625 + 2.0416) = 6 - 3.6666 = 2.3334

Therefore, 7 5_12 - (1 5_8 + 2 1_24) = 2.3334