A random one would be  

45203

We begin by choosing the last, or 5th, digit first.  An odd number must end with
an odd digit, and the only odd ones are 1, 3, and 5, so there are 3 ways to
 choose the last digit.

Next we will choose the first digit.  It cannot be 0, so it is one of these:
1,2,3,4,5, but it cannot be the odd digit that we chose for the 5th digit.
So there are 4 ways left to choose the 1st digit.

The other digits can be a 0, so there are 4 ways left to choose the 2nd digit.
Then there are then 3 ways left to choose the 3rd digit.
Then there are then 2 ways left to choose the 4th digit.

That's 3*4*4*3*2 = 288

Edwin