All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the amount of 5,000 is paid as an installment from the debt owed to your father, then this is permissible but if it was interest and your aunt will pay him the full amount of 10 lakhs when she can, then the amount of 5000 is Riba (interest and/or usury) and it is not permissible for her to pay it and it is not permissible for your father to take it because the one who consumes Riba and the one who gives it to others to consume it are both cursed by the tongue of the Prophet .
Besides, mortgaging the house (to your father) for the debt is permissible but this does not make it permissible for your father to take the rent of the house for himself; rather the rent is for your aunt as the Prophet said: “The Rahn (security) is not forfeited (i.e. it does not belong to the mortgagee as his property). To the mortgager returns its profit and he is held responsible for its loss." [This Hadeeth refers to a forbidden transaction in which the mortgager says to the mortgagee: I will bring you your due money after such and such a timer, if not, the mortgage is yours for what I was pledged for.][Ibn Maajah]
No doubt, the rent of the house is a profit, so it must be for (the right of) your aunt; therefore, that amount should be considered as an installment from the debt, otherwise it is forbidden Riba because any loan that brings any profit is Riba as discussed in Fatwa 90508.
As regards milking a mortgaged animal and riding it in return for spending on it, then this is not the same case, because the milk is produced due to spending on the animal and it is not an obligation on the mortgagee to spend on it, so if he wishes to spend on the animal and milk it or ride it in return for what he spent on it, he may do so. This is not the same case with the house even if it sometimes needs some maintenance, since it is not continuous like spending on the animal. In other words, in principle, it is forbidden for the mortgagee to benefit from the mortgage in any manner, except something that is made an exception by the Sharee’ah like an animal that is used for riding or for its milk. In addition to this, the jurists who are of the view that it is permissible to take benefit from the mortgage, they conditioned that the mortgage must not be for a loan (i.e. it may be for the price of a sold item and the like, but not for a mere loan) so that the benefit would not be in return of the loan, as in this case, it would be Riba.
Finally, the expenses that the house needs may be taken by the mortgagee (your father) from its rent and whatever remains (of the rent) should be given back to your aunt who is the owner of the house unless it is discounted from the amount of the debt.
Allaah Knows best.