Well I don't know south shore but......

Frankly i think 5 Napkin is pretty good - at least when I had it in NYC - havent had it here.
But there are better.
The Backbay Social Club in Boston has a Prime burger that is an amazing experience.  This place is far from a greasy spoon.
And I think Bobby's Burger Palace - (Burlington Mall and Mohegan Sun) are really great.  Mohegan Sun location has liquor license so you can get Bourbon Vanilla shakes etc.  But this is a mini chain and brightly lit etc.

As for ore hole in the wall places - Flat Patties in Harvard Sq is great.  Closest thing to In-n-Out Burger you can get around here.  
Sunset Grill and Tap in Allston is well regarded and divy - I have not been.

There have been a few write ups in the Globe over the yrs about burgers in the area.

Voted best burger in America in Harvard Sq.

www.mrbartley.com

Try KKaties 2 locations Marshfield and Plymouth easily the best burger on the South Shore

ireland you cant buy any where else, I havent been there in like over ten years but i hear they are still around.