First, we need to simplify the expression by following the order of operations (PEMDAS):

Start by simplifying inside the parentheses:
-6(3/37 + 1) = -6(3/37 + 37/37) = -6(40/37) = -240/37

Now, add the remaining numbers:
-240/37 + 77 + 5 = -240/37 + 37*77/37 + 5 = -240/37 + 2849/37 + 5 = 2609/37 + 5

To add the fractions, find a common denominator:
(-240 + 2609)/37 + 5 = 2369/37 + 5

Add the fractions:
(2369 + 185)/37 = 2554/37

Therefore, the final answer is: 2554/37 or approximately 69.041.