This is the barrel rifling for the S&W M&P15 Sporter, what does the 5R mean? And what grain bullets are best for 1:8 rifling?

Everything.  Most versatile twist rate.

+1 why everyone debates 1/7 and 1/9 is beyond me

5r is the type of rifeling. Its popular cause its the same type of twist the remington 700 sniper rifle is, but again those are custom barrels.

Remington started doing that after the freedom group aquired T/C and their 5R tools.

It is a type of rifling that cuts into the jacket on a bullet a lot less.  Less deformation supposedly = more accuracy.  It makes sense to me.  I'm severely debating building my own upper to take advantage of this type of rifling.

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Benefits of 5R: 5R rifling’s unique design provides benefits to the shooter by causing less bullet deformation. How? Because the edges of each land do not cut into and deform the bullet jacket. When the bullet jacket is less deformed, there will be less jacket fouling in the grooves. The results are better consistency of accuracy from shot to shot, greater bullet stability over multiple shots, and ultimately a rifle that’s easier to clean thoroughly.

Mike Rock of Rock Creek Barrels makes 5R barrels also. He makes Denny's/GTS Operator barrels, of which I had one for my Recce. It was a great barrel that really liked Prvi 75gr.

I bought a 5R 1/8 barrel from AR performance. I put 3 rounds of Silver Bear Soft Point into one hole at 50 yards whil trying to sight in for killing piggies.

I got two Adams Arms 1/8 barrels. One middy and the other is a carbine. The 1/8 is great.