To add these fractions, we need to find a common denominator. The least common denominator for 42 and 16 is 336.

Rewriting the fractions with a common denominator of 336:
-19/42 = -224/336
-9/16 = -189/336
-11/42 = -132/336
5/16 = 105/336

Now, adding the fractions together:

-224/336 + -189/336 + -132/336 + 105/336
= (-224 - 189 - 132 + 105)/336
= -440/336
= -55/42

Therefore, -19/42 - 9/16 - 11/42 + 5/16 = -55/42.