-3 5/7 is -(3+5/7)=-3-5/7. We need to be sure whether we add or subtract both the whole number and the fraction or just one of them. Now it's clear that both need to be subtracted.
First, take the whole numbers: -3+5=2. Remember 2 for later.
Now we have -5/7+1/3. Common denominator is 7*3=21.
(-3*5+7)/21=(-15+7)/21=-8/21. How do we make this positive?
We need to borrow from that 2 we remember from before. Take away 1 leaving 1 in the whole number. The 1 we borrowed is 21/21 and we use it to make the fraction positive:
(21-8)/21=13/21. Add this to the whole number: 1 13/21.