7.5 gallons is more than enough for a 5 gallon batch. My kettle is no more than 8 gallons and I have considered doing a 10 gallon batch.
Well yes, but I was unaware that many people, if any, were using large turkey fryers. After reading the original post again, I can see how the OP was referencing extract brewing; I didn't take his beginner status into account because "turkey fryer" usually makes me think about all-grain brewing.
When you brew extract, and potentially partial mash, you don't need to do a full volume boil. This means AT NO POINT do you have to have 5-6 gallons in the kettle. I have done 9 extract w/ special grains batches on my own in my kettle. I never boil more than 3 gallons of water. Some people may like to boil the full volume, but I never have and never will. I view it as a gross waste of time. The bigger the volume, the longer it takes to boil and the longer it takes to chill.
Actually, I've heard that regardless of method (extract, partial, or all grain), doing a full boil if possible is always going to provide a better beer, seeing as how you're boiling all of the malt and hops at full-volume instead of diluting it later. I know there's a lot more information out there supporting this, perhaps one of the more experienced brewers on here like Yooper could explain better.
As for a waste of time, if you can't get 5 gallons to pitching temp in under 30 minutes, that's on the chilling method used. A counter-flow or plate chiller will easily complete this task, and an immersion chiller will typically get the job done. Having to boil/cool 2-3 gallons less of wort doesn't outweigh the advantages of a full-boil.
I steep my grains in about 2-3 gallons of water. I have roughly a gallon boiling to top up the temperature if the steep gets too cold. Then I boil that amount which is never more than 3.5 gallons. When I go to chill, I add the boiled wort to chilled water in the fermenter. This helps my immersion chiller cool the wort as I have just added it to refrigerated water and tops it up to the necessary 5 gallons. I haven't had a bad batch come out of this method and would recommend it.
I've had good and bad batches from extract, and I'm sure I'll have good and bad batches with all grain once I get more time to brew. The biggest factor for most people is all about what kind of space and equipment they have; from there I can only assume (as a beginner myself) that the knowledge and experience shared by the senior brewers here can only help to improve myt brewing.
That said, 7.5 is more than enough for a 5 gallon batch because hopefully you are never boiling the entire volume.
Again, I'd love to hear input from those with hundreds of times more experience than myself about why full boils are always preferable.
Actually, here's a result from a quick search on Google, where Yooper answers said question:
https://www.homebrewtalk.com/f39/full-boil-2-5-gal-351104/
Edit: Oh yeah, full boils also produce more accurate OG readings. Not super important for the first few batches someone makes, but taking readings soon becomes one of the more advanced parts of brewing that home brewers adapt to their method in order to produce better beer.