First Road trip across the US

What to pack depends on when this 5 week Odyssey begins. Obviously a trip during July and August (our summer) will require different clothing and personal items than a trip that runs from October-November (our autumn). Are you planning on renting your camping equipment? If your trip is during the summer months, many of the more popular National parks and recreation areas are booked months in advance.

With five weeks I suggest you do not plan to drive right across ... have 3-4 weeks on the West Coast / Southwest (basically from LA to Denver), and then one week or more around NYC / Washington DC / a bit of New England.

Rent two different cars and take an internal flight.

Camping could be a hassle too ... depends on a lot of things, not the least the time of year, as noted above. On a first trip (that is essentially a road-trip rather than a holiday by a lake) I would use hostels where available, and outside that, the cheap motels that are everywhere.

When is this trip? How many people are you?
Anyone 26 of age or older, most US car rentals require this.

Really depends on your interest and what you want to do and see'
Agree with fly out east for a week to 10 days then fly out west and rent a car or campervan and do a nice loop.

You really don't want to waste a week of your vacation driving across the US, waste of time and money.
Camping is easy and the way to go out wet, IMO. Not so easy out east especially if you want to visit NY, Philly, DC and/or Boston.

Are you experience campers with camp gear?

Agree with the others about splitting your trip between east coast and west coast and fly in between. Internal flights can be pretty cheap, look at Southwest (you have to book on their own website, they do not show up on sites like Kayak and Skyscanner). They are not always the cheapest but allow two free checked bags and have very liberal change policies.

Yes, the time of year is a very important consideration. Weather may dictate where you can (or prefer) to go. And, of course, can dictate what to pack. You may find that it's a better deal to buy cheap stuff in the US instead of trying to haul it with you on a plane. You can donate it to a charity when you leave.

Americans tend to view camping as a way to experience wilderness and nature, not as an inexpensive lodging alternative. So, most campgrounds are away from cities. So-called wild or free camping, where you just set up at a likely looking spot by the side of the road, is usually not on, unless you have permission from the property owner. You could find yourself having an unpleasant 2AM conversation with a police officer or an irate property owner. There are public lands, mostly in the West where you can camp outside of a campground, with some restrictions. These tend to be well off the beaten path.

One-way car rental, where you pick up in NY and drop off in LA, could come with a very hefty one-way surcharge. For rentals of longer than 30 days, the company may want you to exchange cars part way through the trip, so they can do maintenance. You can book a long trip; you just have to do the trade in. Sometimes you can only book long rentals by a phone call, not online.

On another thread, someone suggested thinking of a US visit as two or three separate trips, broken up by plane flights, rather than one big trip. I think that notion may suit you. The money spent on plane flights can be balanced by not having that one-way fee, and by not needing a car in some places, such as NY, Las Vegas, or San Francisco.

Alamo were brilliant with our car hire! Everything from customer service to returning with a scratch (from a bear!).

There are lots and lots of free camping sites, be sure to Google them and our favorite by far was Wildrose camp ground at Death Valley. Look out for the kangaroo rats jumping around at night and enjoy the unspoiled view of the milky way.

Have so much fun!

There are lots and lots of free camping sites

Are these official / recognised free-camping sites, or are they just places where you camped for free?

Check out freecampsites.net. You can camp in unimproved campsites in national forests and some BLM lands.

You can camp pretty much anywhere in a National Forest as long as there are no signs prohibiting it, and most of them are criss-crossed by unpaved roads, so you might consider an SUV, but a car will work most of the time. In general, the closer you are to a city, the more likely you are to be hassled, either by officers, local kids partying, or citizens exercising their Second Amendment rights. As for the National Forest Service itself, a lot of the information they provide is either wrong or out of date (even on their website, or especially on their website), but their rangers are usually friendly and helpful (if you ever encounter one, which won't be often).

I would recommend visiting the middle of the country though. In fact, I would say the further you get from either coast, and away from the cities, the friendlier the people you'll meet. Hostels are a good place to meet other travelers, but cheap motels are smelly, dirty, noisy, and just not worth it. As for packing, it can easily get below freezing in the mountains even in summer so bring a warm jacket, but other cheap items of clothing you may want to purchase here. You can buy a propane stove at Walmart for $20 and a cylinder of propane for $3, and although they usually have the cheapest groceries, I can't recommend most of their camping gear.