Weighted chins for sets of 5 is the best way. But you seem to like high reps, so go ahead.
Once you are already doing 3x5 with weight alternated with 3xBW chinups on the advanced LP and you can do around 20 or so reps of BW chinups. What is the correct way to progress with chinups should weight be added so that you stay in the 10-15 rep range range?
Weighted chins for sets of 5 is the best way. But you seem to like high reps, so go ahead.
I don't think anything is accomplished by a bunch of warmup sets at increasing weight, if that's what you mean. I think you do some bodyweight chins, hit one intermediate set for a double, and then do 3 sets of 5, going up a pound occasionally.