Not an easy ask. Not all these adjectives can qualify similar nouns. Gorgeous is often used as a superlative over beautiful, and generally solely when it comes to female beauty. Handsome is normally used in a male context, so it's not very comparable to pretty, which would normally be used in a female context. Good-looking is not a comparative to handsome or pretty, and it's often used for males. Good-looking and handsome can sometimes be equivalents, but generally is used to indicate the minimum standard of attractive. If one is not good-looking, it is implied they are not attractive, however if one is not handsome, they still may be attractive. Cute generally means something completely different. In gossipy contexts it means attractive, pretty, handsome, hot, or sexy, but most of the time it's a diminutive that means elfish, childlike or endearing which may have nothing at all to do with good looks.

Gorgeous (used more of objects, not people, e.g. This mansion is gorgeous!) Handsome (used of men, while "pretty" is used of women) Beautiful Good-looking Cute