The Grand Canyon is the bottom of what's known as the Grand Circle, starting out at the North Rim (we much prefer the NR) it includes Zion NP, Bryce Canyon NP, Arches NP, Canyonlands NP and Capital Reef with many smaller parks in the area including Petroglyph SP (State Park), Pink Coral Sand Dunes SP, Vermilion Cliffs NM, Dead Horse SP, Monument Valley, Natural Bridges and many others.
Depending on altitude some of these will be hot and others cooler. Arches for one is hotter than Hades and you need to do your hiking in the morning. Carry lots of water with you at all times (at least a liter bottle each). I know you're from FL and think that you are ready for the heat but 95 deg at 10 percent humidity is something we never see in FL.
5 Weeks will mean you have a bit over three weeks in the area. As a driving route I suggest I-10 to MS, up to I-20, across to west of Dallas and US 287. Follow that with I-40 west to AZ and then US 191 north to AZ 264 which will run you thru the Navajo and Hopi reservations. Then follow US 89/alt 89 to Jacob lake and the NRGC. Camping either in the park if you get reservations or at Jacob Lake which has some private CG. If you boondock you can do that in the National Forest just outside the GC gate. You may want to pick 3 or 4 parks to concentrate on so you won't spend your time driving.
If you search the forum for Grand Circle you will find many posts