The recipe calls for my food to bake for 35 minutes at 425 degrees F, But if I have another dish baking at 325 degrees F, how long should I bake the first dish at the lower temperature so it will turn out correctly?
Baking the two together is unlikely to work.
Generally speaking, dishes that cook for a short time at 425F are meant to get crispy and/or browned, or (in the case of yeast or egg-risen baked goods) are meant to have strong "oven spring" from the intense heat. None of these things will happen at 325 degrees; depending on the dish, it will be soggy, greasy, or flat.
I would suggest, instead, cooking the 325 degree dish first, taking it out of the oven and wrapping it in foil and and thick towel to keep it warm, turning the oven up to 425, and baking the second dish. When the second dish is done, you can put the first dish back in the oven for 5 minutes to heat it back up, should it need it.
Of course, a lot of that depends on what exactly those two dishes are, but you should get the general idea.