How many grains in the 5.56 rd?

That depends on which 5.56 round you had in mind.

The original M193 cartridge used a 55 grain projectile.

The current M855 and SS109 NATO standard cartridges use a 62 grain projectile.

The M196 tracer (which complimented the M193 ball cartridge) uses a 54 grain projectile.

The M202 cartridge used a 58 grain projectile.

The experimental XM287 and XM288 cartridges used a 68 grain projectile.

The M856 tracer (which compliments the M855/SS109) uses a 64 grain projectile.

The M995 armour piercing cartridge uses a 52 grain projectile.

The Mk. 262 Mod. 0/1 cartridge uses a 77 grain projectile.