Five gallons is big enough for a baby, but you will need a 10 gallon by the time it is full grown.
For babies, crickets or nightcrawler chunks fed every other day (or every day depending on how young) are good. Wait until they get older to feed things like fish and mice, and then only once or twice a month. Feeding too many mice can case health problems because of the high fat content and also lead to impaction.
Read the caresheet on this forum. Daytime temps should be 80-85 and night temps should be 75-80. Humidity should be around 85%; putting saran wrap over part of the lid helps keep humidity up. You absolutely need a tank heater. If you get a heat mat, put it on the side though not the bottom. You need to get an in-tank thermometer and hygrometer to monitor temp and humidity. Stress from improper housing can make frogs stop eating and even kill them, so you should take care of that ASAP.

Also, from someone living with seven separate reptile/amphibian/fish tanks in a small apartment with a dog and another person: Bookcase. If it's ten gallons or less, get a bookcase, modify it, and tier the setups.

You can use your fish's water dechlorinator to treat tap water for the frog. Take the water out of that plastic container, dip some paper towels in dechlorinated water, and put him on that until you get him a real home. Being soaked in water like that in an air-conditioned apartment could be a death sentence.

I'm really not trying to be rude, but why would you buy a pet without first getting an enclosure for it? Purchasing an animal without even trying to prepare a home for it beforehand is irresponsible.