To find the size of the bacterial population after 5 hours, we can first determine the number of half hours in 5 hours, which is 5 / 0.5 = 10 half hours.
Since the bacteria culture doubles every half hour, the size of the bacterial population after 1 half hour is 2000 * 2 = 4000 bacteria.
The size of the bacterial population after 2 half hours is 4000 * 2 = 8000 bacteria.
This pattern continues, so the size of the bacterial population after 10 half hours (or 5 hours) is 8000 * 2^(10-2) = 8000 * 2^8 = 8000 * 256 = 2048000 bacteria.
Thus, the size of the bacterial population after 5 hours is 2048000 bacteria.