The number of arrangements of $n$ objects taken all a time, when repetition of the objects is not allowed is $n!.$

The numbers formed by $0, 1, 3, 5, 9$ greater than $50000$ can have $5$ or $9$ at the first place.

In both the case, we have four digits remaining for the rest of the four places, which can be arranged in $4!=4\times 3\times 2\times 1=24$ ways.

Therefore, the total such numbers are $2\times 24=48.$