If, as stated, each antellope averages five offspring over a ten year lifetime, the population of antellopes cannot possibly be stable at 24,000 (or any number). Rather, the population would increase fivefold every ten years, ten-million-fold per century, and by a factor of almost 10^70 over the course of a millenium.
Pops. generally cycle about some average num. depending on death and birthrate. The problem is simplified by using the average pop. size. In this problem birthrate = deathrate.
Oops, didn't see the comment about 5 offspring. Sorry.
If we get 0.5 offspring/year/antelope, and it takes two antelope to produce an offspring, then the birth rate is 0.25 offspring/year/antelope. The death rate then has to be 0.25/year; every antelope has a 25% chance of dying per year. I don't see that as a problem.