Thanks for the reply. So, to see if I understand, do you mean I do 5 squats, 1 chin-up, 5 more squats, 1 chin-up etc. for the whole session? I am aiming to do 5x5 and then I am going to try and add some weight but I just can't seem to get past the 3 sets of 5.
I had originally tried something similar to what you suggested. I tried doing 3 chin-ups at the start of the session and then after each exercise but it just meant I was tired for the other exercises. I think what you have suggested is better. Sub-maximal effort and more volume, as you say.