To solve this expression, we need to first convert all mixed numbers to improper fractions.

3 5/16 = (3*16 + 5)/16 = 53/16

2 13/60 = (2*60 + 13)/60 = 133/60

3 27/71 = (3*71 + 27)/71 = 240/71

Now the expression becomes:

3.55 ( 53/16 + 133/60) 240/71 - 38.4

Next, we find common denominators for the fractions in the parentheses:

(53/16 + 133/60) = (1980/120 + 2128/120) = 4108/120 = 2054/60

Now, the expression becomes:

3.55 2054/60 240/71 - 38.4

Now, multiply the fractions:

3.55 * 2054/60 = 1173.7

Now, the expression becomes:

1173.7 * 240/71 - 38.4

Now, multiply the result by 240/71:

1173.7 * 240/71 = 3998.732394

Finally, subtract 38.4 from the result:

3998.732394 - 38.4 ≈ 3960.332394

Therefore, the result of the expression is approximately 3960.332394.