To solve this expression, we first simplify the inside of the parentheses:

7 - 2 5/11 = 7 - 2 5/11 = 7 - (2*11 + 5)/11 = 7 - (22 + 5)/11 = 7 - 27/11 = 84/11 - 27/11 = 57/11

Now we have:

3(57/11) - 11 3/11 + 5 7/11

= 171/11 - 11 3/11 + 5 7/11

Now let's convert the whole numbers to fractions:

= 171/11 - 11 3/11 + 5 7/11

= 171/11 - (1111 + 3)/11 + (511 + 7)/11

= 171/11 - 121/11 - 33/11

= (171 - 121 - 33)/11

= 17/11

Therefore, the final answer is 17/11.