If you have a number ending in five:
$$10x+5;x\in \mathbb{N}$$
You can just take the string of digits before the 5, square it, multiply it by 100 and add 100 times the initial string of digits. Finally you add the 25.
For example:
$$35*35=(100*(3*3))+(100*3)+25=1225$$
When you type 35*35 into Google it tells you 1225, which proves that this works, but I don't know.