I do 5 sets of 10-15 reps of pull ups using a 20lb weight vest. I'm looking to focus on strength and just ordered a dip/pull up belt to add plates. What's a good progression to add strength? Should I aim for 5x5 and increase weight until I can just about complete?
The standard progression I've seen is to add weight once you can do fifteen or twenty unweighted. One then does three or more sets with added weight. One should be able to do at least five and no more than twelve reps--as long as the weight is within those bounds, it's the right weight. This keeps both volume and strength up. If you can't do five, reduce the weight. If you can do ten or twelve each set, add five pounds.
All numbers assume dead-hang, full range of motion, no kip, chin over the bar and hopefully chest touching the bar.