Hello Neeki,
The question of "Leave" (leave with pay) does not arise if he is a fresh appointment (irrespective of when he had left the company previously). No law in the statute governing "employment" speaks anything about not rehiring an associate. This is an internal prerogative of an company whether it can rehire / re-employ an left associate and is generally mentioned in some or the other company policy or could be a prevailing practice.
Now, if the employee had left the company before 1 - 2 month, you should have done his Full & Final Settlement and the employee should have acknowledged the same. (hope you would have also considered his "balance leave/s", gratuity-if applicable, bonus-if applicable, other applicable dues while preparing his F&F and would have paid the F&F settlement amount to him).
For you to do his Full & Final settlement, you should have received the resignation from the employee (unless it is a case of termination / retrenchment).
If these events have occurred in a sequence, it's clear that the employment had got terminated and that it is a case of re-hire / re-joining.
Again, as per what Suresh has stated, you should have issued a fresh appointment order/letter to the associate which should have been acknowledged by him.
In such a scenario, the employee's claim for having taken 5 leave (I believe he means 5 weeks) is irrational.
Cheers,
A.B.