I agree with the previous poster, 10% may be a reasonable amount. When a court looks at late fees, it looks to determine whether the fee is a penalty for late payment or a form of liquidated damages (assumed damages suffered by not having the money in hand on the due date). Because landlords often have to pay things like property taxes, sometimes water bills, etc, not having the rent by the due date may mean that they will themselves suffer late fees. A court will most likely rule that a 10% late fee is a reasonable assumption of damages suffered and not a penalty, and thus valid. If the court rules that it is a penalty, it may be void. But, 10% has been viewed in the past as a very reasonable amount.
This answer is for informational purposes only and should not be construed to establish an attorney client relationship. Before taking any legal action, it is always advisable to discuss your specific situation with an attorney.
There is no statutory limit on late fees, but it has to be reasonable. According to a colleague of mine, $50 or 10% of the rent is reasonable (whichever is higher).