It took almost 125 years for the human population to increase from 1 billion to 2 billion (during the 19th century) - when the population is a third as large, the rate of increase is even smaller. 5 years is a pretty short timespan - I'd guess we're talking a couple of percent, at best. (If you want to consider the fact that humanity is still cleaning up after a decades-long war, it's probably even lower than it would be in peacetime - it's not like we have nothing to do but sit around and make babies - or take care of them.)

I think using the one hard number we've been given isn't going to steer you too far wrong.