I bought this SS a week ago and I’m starting to work on it. Pulled the plugs just to see what they looked like and they were NGK TR5GP which on all websites I check do not fit a 305 V8.

I know the previous owner has done some work on the engine but it looks like the original 305 to me…am I missing something or is it running the wrong plugs? Is this as big of deal as I feel it is?

The distributor cap and plug wires look new. I still need to verify if either are also incorrect.

Edit: Didn't realize the title got cut off...but just stating that I think the previous owner used the wrong plugs.

 

Yes, he used the wrong plug's I can't even cross them to AC Delco.Put some AC Delco plugs back in it and enjoy driving the car.

 

This plug does fit Chevrolet small block engines. Since there's no physical damage to the electrodes, I wouldn't say it doesn't fit, but it's not in the heat range for your application.
NGK's TR5GP is a moderately hot plug; 5 on a scale of 1-12 with 1 being the hottest. For your application, the manufacturer lists a heat rating that's one step hotter; 4. I would guess the previous owner may have had knocking and/or run-on issues and may have thought going with cooler plugs would help. Nevertheless, if the engine's stock and you intend to keep this car, I would go with iridium plugs in the correct heat range such as the NGK UR4IX.
The distributor cap seen in your photo is correct. If the plug wires are at least 8.0mm then you're good to go. If you can go with a taller air filter element, I would encourage you to do so.