You can do extract brews. Buy a cheap 5-gallon kettle.
The OP stated that his stove could barely handle a 7 qt pot. So a 5 gallon pot isn't going to work. Th OP also stated that he wanted to use grain, not extract.
Question for the OP:
Does your stove have multiple burners? Can you run two pots at once? What do you consider "special equipment"? Does that include buying another pot? A bigger pot might boil if you leave the lid 1/2 on.
If getting a better stove or a propane burner isn't an option, the answer is to make concentrated wort and water it down or run multiple mash/boils to get 5 gallons.
Get a cheapo 16 quart pot (or go to 5 gallon if you want) and a BIAB bag. Mash 5 lbs of grain in 3 gallons of water. Divide your wort and boil both pots, cool and add to the fermenter, repeat and you'll get about 4 gallons of concentrated wort, you'll have to add a gallon or so of water. You could even add the water when the wort is hot to make sure its sanitized. You'll have to play around with it to get your numbers right, and you'll probably have to adjust the hop additions,
your boil off rate + absorption by the grain will determine how much water to add.
Note that some large industrial brewers use the concentrated wort and add water later method. This is done to increase production and overall efficiency, but may or may not change the flavor of your beer at the homebrew level.
Of course you could use your existing pot and make 3 concentrated batches and then add water to get 5 gallons. Take a 5 gallon batch, split the grain up in thirds and go for it. Again you'll have to play around with volume and hop adjustments until you figure out a system.
If there is a will, there is a way.