To add these fractions together, first find a common denominator:

The least common multiple of 11 and 17 is 187.

3 5/11 = 38/11
3 8/11 = 41/11
1 5/17 = 22/17
5 13/17 = 98/17

Now, convert all fractions to have a denominator of 187:

38/11 = 38 17 / 11 17 = 646/187
41/11 = 41 17 / 11 17 = 697/187
22/17 = 187/187
98/17 = 98 11 / 17 11 = 1078/187

And add them together:

646/187 + 697/187 - 187/187 - 1078/187 = (646 + 697 - 187 - 1078) / 187
= 78 / 187

Therefore, the result is 78/187.