The answer is no.
8 minus 3 7/10 would equal 5 3/10, not 5 7/10.
You can check this by adding 3 7/10 plus 5 3/10 or 5 7/10.
You will see that the first one will give you 8, meaning it is the right answer and your friend is wrong, the second one adds up to 8 4/10, which is not right.
Hope this helps!