The other answer is incorrect.

We find the numerator of the probability.

In order to have two vowels (a,e,i,o,u) and three identical
digits, such as, say,

EU777

We can pick the vowel for the first character any of 5 ways.
We can pick the vowel for the second character any of 5 ways.
We can pick the digit for the last three characters in any of 9 ways.

That's 5×5×9 or 225 possible successful tags

So the numerator of the desired probability is 225.

Now we find the denominator, which is much much larger:

We can choose the 1st character, a letter, in any of 26 ways
We can choose the 2nd character, also a letter, also in 26 ways.
We can choose the 3rd character, a non-zero digit, in any of 9 ways.
We can choose the 4th character, a digit, (possibly 0) in any of 10 ways.
We can choose the 5th character, a digit, (possibly 0) in any of 10 ways. 

That's 26×26×9×10×10 or 608400 possible tags, successful or unsuccessful..

So the denominator of the desired probability is 608400.

Probability =  = .

Edwin