A single #10 nail has a shear strength rating of 80 pounds.
4 5/8" brackets ought to be able to hold up several hundred pounds provided they are properly installed.
As long as your cabinet cannot flex outward, your 5/8" brackets ought to be excellent. If you have 2 screws on each bracket, then you have 8 screws. If your monitor weighs 80 pounds, then you only have 10 pounds on each screw.
Bob