As weird as it seems, 5 years is not a long term investment. Furthermore investing is about accepting risk. Based on your criteria for the alternative to a down payment, I think your only choice is to make the larger down payment.
If however, you were willing to invest that money for the long term (in a retirement account or an educational account for example) then I would definitely encourage you to invest. I think the chance that a long term investment in a diversified investment account will exceed 3.25% is pretty high. However, that is only my opinion, and I am not clairvoyant, so your let your personal tolerance to risk be your guide.
But again, based on the way you asked it, down payment all the way. Your time frame means you are not an investor. Therefore your only option for risk free storage of money is an FDIC insured account, which might pay a little less than 1% for the next 5 years. A bigger down payment will have a 3.25% return in this case.
Also, make sure the following is true:
- Taking any match available at work via a 401K
- No unsecured debt (like credit cards) or bad debt (high interest car loans or student loans)
- A fully funded emergency fund that is 6 months of your expenses. Especially important if you own a house.
- Pay off any other loan (student loan, car payments or peronal debt)
- Maxing out a Roth IRA if you are eligable
- Maxing out a Traditional IRA
- Spending some of your money to have fun.
In that order. #4 and #5 could be swapped if the interest rate on the loans is really low.