20% down (80% loan-to-value (LTV)) is the standard minimum for avoiding mortgage insurance. If you're willing to pay a mortgage insurance premium, 5% down (95% LTV) is not uncommon AFAIU, especially for large, "jumbo" mortgages, at least in coastal California. (Elsewhere it's probably the case that jumbo mortgages require a greater equity stake, not lower. Coastal California is a little unique. While prices are nuts, the risk of a significant valuation crash is negligible compared to, say, Nevada or Florida, so issuing banks are more comfortable with the additional risk and seemingly more eager to have that asset in their portfolio.)

Also, in case there's some confusion, "deposit" and "down payment" are distinct. In American real estate parlance a deposit is earnest money (often 5% of the initial offer) to bind the seller into closing--the process of finalizing contracts among all involved parties, and transferring assets. A deposit might be forfeited if the buyer pulls out. A minimum down payment is the minimum equity a mortgagee (e.g. bank) requires the borrower to hold in the property as a condition of making the loan.