Briggs 5 HP Engine model 1352020258-01 Bad Gas and rusted tank

Years ago I had a car gas tank which I cleaned and relined. The procedure should still work, as long as there are no holes.
 
Remove the tank. Insert things to jiggle around and rough up the inside of the tank. I started with a heavy chain, but your tank is small. Try rough stones or coins, maybe an old chainsaw chain. Shake, shake, shake, really bang them around, then pour in a little soap and water, slosh, and drain. The water will come out rusty. Repeat until the water is clear. It will take quite a few tries, so be patient. Then go to the car parts store and ask for liquid with which you can line your tank. Pour it in, slosh it around, and pour it out. Let the coating dry. Repeat a few times until you're pleased with the thickness of the coating. Make sure it's really dry before you pour gas in. I'm sure the stuff comes with instructions.
 
When you're finished and really to mount the tank again, make sure to install a little inline fuel filter, if possible. This might not be possible on some old Briggs and Stratton engines where the carburetor in mounted right on the tank and sucks fuel directly from the tank without a gas line.

Another idea would be to try to find a good used tank. Many motors used the same tank so if you had some place near by that works on small engines they may have a tank sitting out back in the dead engine spot!
 
Maybe if you could post a picture of your tank here someone would have one they would sell to you for less than the cost of the sealer kit!