-6 9/20 + 5 5/8 - 10.39 =

Converting the mixed numbers to improper fractions first:
-6 9/20 = -6 + 9/20 = -6 + 9/20 = -120/20 + 9/20 = -111/20
5 5/8 = 5 + 5/8 = 40/8 + 5/8 = 45/8

Now, the equation becomes:
-111/20 + 45/8 - 10.39

To add fractions with different denominators, we need to find a common denominator. In this case, we can use 40, which is a multiple of both 20 and 8.

-111/20 2/2 = -222/40
45/8 5/5 = 225/40

-222/40 + 225/40 = 3/40

Now the equation becomes:
3/40 - 10.39

To subtract a decimal from a fraction, we first need to convert the fraction to a decimal:

3/40 = 0.075

Now, the equation becomes:
0.075 - 10.39 = -10.315

Therefore, -6 9/20 + 5 5/8 - 10.39 = -10.315.