How much boost can a stock 5.3 handle?

We don't publish a single boost number: safe boost depends on the turbo size, intercooling, fuel (E85 vs pump gas), timing and the engine's condition. Use horsepower, not psi, as the target. Speedway's turbo 5.3 recipes reach 600 hp with mostly bolt-ons and 700 hp with valvetrain upgrades (cam, LS7 lifters, head studs), with no pistons or rods listed. Size the fuel system for it (≈78 lb/hr injectors for 600 hp turbo on gasoline, 94 lb/hr on E85, per Speedway's chart) and get a professional tune.