Consider the number of ways to draw 5 unordered numbers from a set of 53.  nck(53,5) leaves us with 2,869,685 combinations.

We can determine the number of ways to draw 2 odd and 3 even numbers from 53 with nck(27,2) * nck(26,3).  This gives 912,600 combinations.  Divide by the total number of combinations to get the probability (31.8%) and divide this probability into 1 to get the odds (1 in ~3.14).