If you belong to a nation of 5000000 people, and the world population is 7000000000: What is the odds for being born in this nation?

Not agreed, we have a huge number of immigrants who have become nationalized.  they belong to our nation but they were not born here.  Sorry reinout-g I only just read your next sentence.

I am nit picking too.  The world population is still irrelevant.

Stupid illogical school problems.  Just give the teachers what they want - that's how you pass a test!

you could always be clever and state why the question is stupid and then give the teachers what you think they want  (or vice versa).  I'd probably do that!

The chance is 5*10⁶/7*10⁹ or 5/7000.  That is, there are 5 chances in 7000 of being born in that nation (or 1 in 1400 if you prefer).  

The probability, (if that's what's being asked), of being born in this nation is 1/1400, the odds are 1399-1 against.

I know I'm nitpicking but if you belong to a nation, isn't the probability that you were born in it 100% (if we do not take emigration into account)

Agreed, but like many of questions in this forum, guessing what the question is is part of the question, (if that makes sense). Just because a questioner asks a particular question (or not) it doesn't follow that that is what the questioner intended (or not). Is that last or not needed ? Probably not.