My Skittles is 'free-flighted', so he's not used to being caged- but I've kept him in his day cage for as long as five hours and he seems to do fine. I actually have a harder time being away from him than he does. lol.
I think the fact that he'll have an hour in the morning and five at night is just fine. The only suggestion I would make is to ensure your conure has enough toys they like to keep them occupied. I'd also leave the radio or tv going.
I don't foresee any problem with the schedule you plan on keeping.
PS, like others have said- pictures are a must here. Otherwise, you'll get bombarded with demands over and over so best to just surrender to our demands now and provide the pictures. (I'm being sarcastic, btw)- lol.