I had plants hanging from the ceiling with toggle hooks, each of which needed a 5/8" hole. What's the best way to fill them in & make it look good again?
"the best way" is super subjective, as some want easy; some want quick; some want perfect.
Since you said "make it look good", I would recommend traditional spackle (as opposed to "lightweight spackle") applied with a wide putty knife, with fine sanding between the several (at least two) applications and after the final application.
If you had said "make it look perfect" I would recommend high quality drywall topping compound, applied with successively larger drywall knives (to feather the repair area and make it near-unnoticeable in all lighting and gloss conditions) and applied and sanded in several coats as mentioned above.
The repair will likely be noticeable regardless, if your existing wall has any sort of texture and/or if you use glossy paint. There are ways to make it near-perfect but it usually means repainting the entire wall.