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Since there are 5 born per decade, 5 die per decade. The population just didn't pop up and start all in phase, it contains animals of all ages.

If there are five antelopes born and five antelopes dying per decade, the average lifespan is not ten years--it is two years.

Consider: in a million years (number chosen large so as to render phasing effects trivial) there will have been 12,000,000,000 antelopes that lived, 24,000 at a time, a total of 24,000,000,000 antelope-years. It doesn't matter whether some animals lived for millenia while others lasted only minutes. The total number of antelope-years accummulated will be 24,000,000,000 (since a herd of 24,000 antelope will accumullate 24,000 antelope-years per year) and the total number of antelope will be 12,000,000,000 (birth rate of 5 antelope per antelope per decade). Thus an average of two antelope-years per antelope, or (more simply), two years.

Another question.Forgetting that there has to be some males in the population,taking the 24,000 number at 5 births per 10 year lifespan what is the population growth.
Taking the stated constant of 24,000 living for 10 years every year 10% of the population die equaling 2,400 animals.Of the remaining 21,600 half are not reproducing leaving just shy of 11,000 new births/year.
It would seem the birth/lifespan/death rates to maintain a population of 24,000 are much to high.
Of course in reality some of the births,which should over time be about 50%,would be males which would half the numbers and make the equations more plausible.

Corrections requested if I have calculated incorrectly.

" If there are five antelopes born and five antelopes dying per decade, the average lifespan is not ten years--it is two years."

Depends on how many 5-12 y/os I package each year and their age distribution. Harvests vary from year to year. Averages are taken over a wide enough window to smooth out the bumps. Hard winters, drought, disease can also take a toll periodically. In general any particular ecosystem can only support some stable population. Dieoffs tend to be the rule that maintains it. The young and old are the most probable to die off. The average age is essentially constant.