How is the Zakat calculated for a joint sum of money between spouses, designated for purchasing a home, which reached the nisab and was not known until five months after reaching it, given that the wife has separate funds in a separate account, and the husband has moderate debts?

Each of you has an independent financial liability. Therefore, each of you must pay zakat on the money you own if it reaches the nisab and a full Hijri year has passed over it. The determining factor is the money reaching the nisab, not the time of knowing the religious ruling.

As for money saved from a salary, it is an acquired asset, and its zakat has specific details.

Regarding debt, there is a difference of opinion among scholars regarding its deduction from zakatable wealth.