The number of numbers, strictly between 5000 and 10000 can be...

Given,

Numbers $1, 3, 5, 7, 9$

Now to form number between $5000 - 10000$

\begin{cases}\mathop{\mathop{_}_{⏟}}_{5, 7, 9} & \mathop{\mathop{_}_{⏟}}_{4\text{ways}} & \mathop{\mathop{_}_{⏟}}_{3\text{ways}} & \mathop{\mathop{_}_{⏟}}_{2\text{ways}}\end{cases}

Here at $1000 ' \text{s}$ place should be taken by $5, 7 \text{ and } 9$

So for $1000 ' \text{s}$ place there will be $3$ ways,

Now for hundredth place there will be $4$ ways,

For ten's place there will be $3$ ways,

And for unit place there will be $2$ ways,

So total ways will be $3 \times 4 \times 3 \times 2 = 72$ ways.