Can anyone identify these moths? Is it safe for them to be out in the daytime In direct sun?

Ok Here’s My Dilemma-

I have a pergola in my yard that I have a Moonflower Vine living ceiling (ok so it’s My first try at it and I made some mistakes so this year it is not even close to a ceiling - but next year it will be a living blooming ceiling for sure!!!) and I draped mosquito netting and lace over the top.

I have several nightime visitors fairly regularly Who love the moo flowers. After some research and so very close encounters- I believe I identified them correctly as 5 spotted hawk moths. If anyone can verify or correct that I would be obliged!

long story short- they have come (one at a time) and hung out with my and my friends in the pergola at night. I have also had to rescue them from the netting bc they keep the wiggling into the folds at the top.

Its Extremely open air- plenty Of ways to enter and exit and they keep getting Into the folds. My concern is that they seem

nocturnal and idk if they can be out in the sunlight during the day or if they’ll bake!

Any input would be appreciated!!