A PubMed search turns up no trial of rep schemes for band assisted pull-ups, so five to eight is a coach's starting point rather than a finding. The sets and days come from general strength guidance for healthy adults. The rule for moving down a band is what turns those numbers into progress.
Five to eight reps keeps the work hard
Your first pull-up is a single hard rep. Long easy sets are a different job. In a review of the research, heavier loads led when strength was tested with a one rep max, partly because that training is closer to the test2. Applying that to a band is a coach's reading, since the review covers loaded lifts rather than assisted ones. A band that stops you around eight keeps each rep demanding. The same review found muscle grows across a wide range of loads, so you give up nothing there2.
Fewer than five full reps means the band is too light for now. If you can go well past eight, it is giving you more help than you need. One test set will find the right band.
Two or three sets, at least twice a week
The American College of Sports Medicine advises healthy adults to do at least two sets per exercise and to train each major muscle group at least twice a week1. Start there. Rest until your next set can be full reps. In one meta-analysis, resting longer than a minute gave a small benefit for muscle size, with no clear gain past about a minute and a half3.
Count only the full reps
A rep starts from straight arms with your shoulders set, finishes with your chin over the bar, and returns slowly to straight arms. When a rep stops short, the set is over and that rep does not count. You do not need to grind on to failure. The same position stand found it adds nothing to gains in strength or size1.
Move down a band when every set earns it
- Reach the top of the range. That means eight full reps on every set in the session.
- Rate every set Clean or Fair. Clean means every rep was full and under control. Fair means it was hard work and your form held.
- Move to your next lighter band next session. Expect your reps to fall back toward five. That is normal, and you build back up from there.
A rough set does not earn the step, even if the reps were there. That is no failure. It means the band you are on still has something to teach you.
On the day you step down a band, add no set. A lighter band is already a harder session, so change one thing at a time.
Keep pulling, and lower slowly
Slow lowering from the top is good extra work, and it does not replace pulling. In a study of strength trained men, the biceps, forearms and chest were more active on the way up than on the way down4. Keep your band reps, and take your time on the way down in each one.
When your lightest band runs out
Once you are on your lightest band and your sets are clean, try a pull-up with no band. Do it right after your warm-up, while you are fresh. Give yourself up to three tries, with all the rest you need. If it does not go today, do your usual sets and try again another week.