The number of three digit odd numbers that can be formed with $1,2,3,4,5$ is

The last digit can take one of these $3$ values, $1,3,5$ if the no. is odd.
The remaining $2$ digits can take any $2$ of the remaining $4$ digits.
Total no. of ways $=3\times {}^4{P}_2$
$=3\times 12$
$=36$