I go with the sunroom, too, and here's why. You can build a shed for cheap at some point, and until then you'll probably keep one car inthe driveway, and all the bikes and basketballs in the garage along with the yard and snow tools. The sunroom will make a great playroom while the little ones are little. I've seen that sunroom with nothing in it but a low-pile play rug and Lego. Or balls. Or plastic hockey sticks. Or those big Little Tykes (slide, trikes, trains) Or Hot Wheels. Or dollhouses. Or art projects (easy-to-clean tile floor). Usually just one or two of those. But a great playspace, near you but not, outdoors but not. After they are done with those types of toys, it can be dining space and added living space. You don't need the shed until Boy #1 gets a car. Oops, didn't mean to scare ya lol! Upstairs, I wonder if you can steal some space from the game room to make a reach-in closet for Bedroom 2, and use its walk-in closet to expand the bathroom. 5 boys will need more counterspace, more drawer storage, and (I can't believe I'm saying this, I'm usually a 1-sink gal) 2 sinks. Downstairs, consider eliminating the study closet and adding a shower to the powder room.

Get a pro KD and contractor on your site. ASAP. and don't waste time seeking online opinion of which there will be a thousand. ..................and not all will even be feasible. The "layout that makes sense" is one you develop WITH the designer, not a cabinet seller. It is in consideration of all that is on your wish list, and also what is possible within the space. Possible is partly a budget function, load bearing wall function and other things as well. What makes the most sense, is to EXPLORE those possibilities with a pro, ON your site.

IMO the sun room would be a better spot for LR type use and the TV in the space next to the kitchen. I think too many windows that will require to much window covering to cut glare in this space . BTW the area near the kitchen also a better place for a playroom . I like spaces for adult conversation out of the kitchen area.

A narrow entry door is also a limiting factor. Is the exterior door from sunroom wider? Usually exterior doors are 36” wide. So that gives a way in. Plus, some of the swivel bases can be removed which would help. I can’t be sure without careful measurements. I would prefer a cozy love seat and one swivel chair. For several reasons. First, your “line of sight” coming into this room is looking at shorter wall. That is your focal point wall. The cozy loveseat you can curl up on with a book, would be my choice. Then perhaps a “C” table near the loveseat with an arc lamp that can be positioned over reading spot. Add art on that wall. Then you could position two compact chairs for added seating across from that piece. Small drink tables and that’s it. Might add cute small ottoman that could act as small table with a small tray when needed. Just depends on how you realistically will use this room.