No need to get into a lot of detail to explain the example. The half-life model says that if you have a certain amount of a drug present at the start, say X, then at some future time you will have some fraction of X left, with the fraction determined by the elapsed time and the half-life parameter, and independent of the starting amount. So if you're comparing starting with 100 mg versus starting with 500 mg, then the remaining amount is always five times greater with the larger starting amount. Suppose the fraction remaining is one percent after one month. Then starting with 100 mg you're left with 1 mg after a month, whereas starting with 500 mg you're left with 5 mg. In either case you're left with the same fraction of the starting amount. In the case of an elapsed time of five half-lives, this fraction is assumed to be small enough to neglect, about three percent.