So van life throws in a fairly unique set of hurdles. Do you have any 12v stuff already installed? Do you really NEED a 5000w inverter? What kind of loads are you looking at that will physically fit in a van?
As an example, we had a member on here a while back trying to design a tiny home system. He grabbed the Power Audit form from the Resources section and filled it out a few times (do this first!!!) and kept coming up with nearly 10,000w of inverter. I pointed out that if he promised NOT to run the espresso machine, the frother, the microwave, the blender, AND the hair dryer at the same time, he was well covered with a 3000w unit. Thinking about the loads is critical, but so is how you're going to be USING the loads is also vital.
I have yet to see anyones build for a van on here exceed a 3kw system. That's still enough power to run a hot plate AND a mini-split at the same time.
The size of inverter you need is going to determine a LOT about the rest of the system. Physics is also a major factor because while 800ah of batteries and 4000w of solar panels sounds great, I doubt you have that much room to work with.
The other big concern is budget. How much can you realistically spend on just the power system after getting the engine tuned, new tires, furniture, bed, appliances, etc. There are some places you can shave costs (inverters, batteries, panels, etc) and some places you can't (converters, fuses, wire, breaker, etc) that all have to be balanced.
Another big hurdle is heat. When it comes to making anything hot (water, food, the living space, etc) the general concensus is "Anything But Solar" because heating things takes a lot of energy both in wattage for the elements, and capacity to keep pumping that wattage over time. Spaghettie-O's aren't as tasty in the dark. A recommendation for that (because I'm a whore) is a diesel parking heater. Yes, it may be another fuel you have to have, but a 5kw unit on low will cook you out of a van in nothing flat, runs on 12v power, and sips fuel. I've seen over 10 days on low out of some of mine on a single 5gal jug of diesel. Just a thought. As for cooling, a mini-split is WWAAYY more energy efficient than any of the roof mount RV styles unless you spend $$tupid money on one. If you can find a little 6kw somewhere that will likely be plenty, especially if you've insulated your walls & ceiling. A little complicated to mount some times, but works great!
Just a few thoughts off the top of my head.