If you've ever had shoulder or back problems you know how much that sucks, so why not engage in some preventative care.
So without further ado check out this article by Nate Green: Things You Should Know How To Do.
In the article I lay out a sample program for getting someone from 5 pull-ups to 10.
WEEK 1
Workout 1: Band-assisted pull-up with a medium band, 3 x 8.
Workout 2: Dumbbell row, 3 x 8-10. Don't work to failure — leave 2 reps in the tank on each set.
WEEK 2
Workout 1: Band-assisted pull-up with a medium band, 3 x 9.
Workout 2: Dumbbell row, 3 x 8. You should be close to failure on the final rep of your final set.
WEEK 3
Workout 1: Band-assisted pull-up with a medium band, 4 x 8.
Workout 2: Dumbbell row, 3 x 10, using the same weight you used for Week 2.
WEEK 4
Workout 1 (test day): Body-weight pull-up, 1 x max reps.
Workout 2: Dumbbell row, 2 x 15.
WEEK 5
Workout 1: Body-weight pull-up, 3 x 4 with slow negatives on reps 2 and 3.
Workout 2: Inverted row, 2 x 8. (If you don't know how to do this one, check out this article.
WEEK 6
Workout 1: Body-weight pull-up, 4 x 3 with slow negatives on reps 2 and 3.
Workout 2: Inverted row, 3 x 8.
WEEK 7
Workout 1: Body-weight pull-up, 4 x 4 with slow negatives on reps 2 and 3.
Workout 2: Inverted row, 3 x 10.
WEEK 8
Workout 1 (test day): Body-weight pull-up, 1 x max reps.
Get to work!