Consider the following:
1. Given that you don't know how much time goat's pregnancy takes, knowing it is a mammal you should know it wouldn't be less than a couple of months, and probably not much more than 1 year. Assuming 1-2 (so an average of 1.5) pregnancy per a year per a female goat is fair.
2. We start with one female goat so year one is 1.5 *1, year to could be assumed as 1.5 * 2
(we round up the7.5 = .5 probability of having a female born times 1.5) and we add the number of males, which is always assumed to be the same num of females (so 2); total 2*1.5=3+2=5
3. Continue: 5+(1.5*2.5)+2.5..... n+(1.5* n/2)+n/2... 10+(1.5*5)+5
The number itself does not matter in this case, as long as you are not making an order of magnitude mistake. What matters is that your express explicitly your assumptions, flash out the model you are thinking of and reason through it. Good luck!
Goat's pregnancy is indeed 5 months. Life expectation is 15-18 years (so irrelevant here).