Chances of getting 5 golden legendaries in a single pack?

Solution 1:

Yes, the math is right. The chances of having a golden legendary is 0.05% (1 over 2000).

So, that's exactly 0.05% x 0.05% x 0.05% x 0.05% x 0.05% = 3.125e-15% chances that happens, that is to say once chance in 3.2e+14. In other words, you have to open 150 thousands of billions packs (in average) before hoping to open the 5-golden-legendaries pack. Good luck !

EDIT: The math is right if you consider no pity timer (thanks Rob). As Blizzard does not provide any detail about this, the straight-forward calculation gives a nice idea of the chances to have such a pack.

Solution 2:

Only considering your information you would be correct. Your information assume that any probability of a card being a (golden) legendary is independent from the probabilities of other cards.

However, this doesn't seem to be the case. On reddit somebody analyzed the probabilities of getting legendaries. Quote:

The probability is increasing as the amount of packs increases and it also shows a significant gain after 30 packs.

I don't know if there is some official source confirming the existence of such a Pity Timer as it is called there.

Thus, the probability of getting a legendary appears not to be the same for every card and, consequently, does not seem to be independent from other probabilities. That means the calculation is probably much more complicated than just (0.05%)^5.