Pretty easy to do on the first stage. You may be able to do it with less, but I got the first 3 health upgrades first before I could get it where the last shot wouldn't kill me without hitting the 5% mark. Best way I found to drain health in a controlled matter was letting the waves of small green planes run into me, as each takes 4-5% off your health. I recommend the first stage because it's super easy so not getting hit after you're down to the mark shouldn't be difficult. Will pop after beating the boss.
Also, the description is slightly misleading. You don't have to be lower than 5%, as being exactly 5% will work as well.