EMOM or "every minute on the minute" training is the best method for improving pull-up strength and endurance if you're stuck around the five rep mark. All you need to be able to do is two consecutive pull-ups. Two, that's it.
Get your timer ready and prepare for a ten minute EMOM. At the beginning of every minute, do two pull-ups. Start with about 30% of your max rep set of pull-ups and build from there. So, if 5 pull-ups is your max, just do 2 pull-ups every minute on the minute, for 10 total sets.
From here you want to increase volume slowly. Pull-ups respond well to progressive loading, but if you add reps too quickly you'll stall out or sacrifice good form. Here's an example of a three week progression for someone who can do 5 pull-ups:
So you add five reps per week to the total amount of pull-ups by adding one rep to the first five sets. As long as you add at least one pull-up to your total number each week you're making progress. When you can no longer add reps each week it's time to retest your max rep set and start the process all over again.