Is it permissible for a husband to utilize the money of his wife's orphaned child for a period of five years, provided he writes a promissory note and pays due interest, as an alternative to dealing with a bank?

It is impermissible to approach an orphan's wealth except in ways that are in their best interest, and "best interest" means what is most beneficial to them. It is not permissible for the guardian to dispose of an orphan's wealth or borrow from it for their own personal benefit without benefit to the orphan. It is also not permissible to borrow from it or benefit from it in exchange for interest, as this is usury (riba). However, if the benefit is through trading or speculative partnership (mudarabah) such that the profit is shared between them according to a known percentage, then this is Islamically permissible, based on the saying of Umar, may Allah be pleased with him: "Trade with the wealth of orphans so that zakat does not consume it." It is permissible for the guardian to give the orphan's wealth for mudarabah, or to manage it themselves in mudarabah, or to invest it and hire someone to manage and trade with their wealth, or to buy their wealth from themselves if that is better for the orphan. It is advised to stay away from an orphan's wealth, especially if one is not their guardian.