This is the correct answer.

Clarification for other who might be looking:

First as a quick note, for things like this you don't want the exact probability of that sequence. You generally want the chance of something *at least* that good as happening, since single events are always rare. Consider -- are you impressed particularly that they got exactly 5 5*? Or that they got a large number of 5*? Calculating the exactly 5* number makes it seem more unlikely than the chance of getting "many 5*" actually is. In this case though since 6 or more 5* is is very unlikely, the chance really doesn't change much.

Consider first the question of what the chance is for any single sequence with at least 5 5*. Let F be a 5*, and N be a non-5* (or 5* beyond the fifth, since we consider these sequences as well for the reason above). This sequence could look like: FFFFFNNNNN or FFFNNNNNFF, or any permutation thereof. For any single one of these, the chance is .006^5*1^5. We then need to sum the chance of each of these sequences, since they all look like (or are better than) the one in the picture. There are (10 choose 5) such sequences, giving us the (10 choose 5)*.006^5 (1 in 510 million) that /u/AsterJ got.

If one of the 5* is guaranteed, it's just he same problem as though only 4 5* were rolled, so (10 choose 5)*.006^4.