Can you compute the price of a 5-year zero coupon bond from 2 5 year coupon bonds?

If the 2 5 years are exactly the same with the exception of having coupons (same lender, same claims, same everything) then yes you should be able to. The trick is finding the right yield curve and discounting everything back to the present value. The coupons can be treated as mini zero-coupon bonds in their own right.