"What should my exposure time be if I take a picture every 10 seconds?"
Your exposure time should be 'whatever it needs to be' in order to get as close to the 'proper' picture exposure for the environment you're in as possible. In practice this will be impossible to get completely correct (without the use of an external homebrew realtime light meter and intervalometer... which is what I use. Shoot me a message if you're a DIY electronics guy who is up for building your own equipment and I'd be happy to point you to some excellent resources...), because the light will be changing constantly throughout your trip, but you can set it so that the fluctuations aren't too extreme, and then adjust it throughout the day/trip as the lighting changes, paying special attention to dawn and dusk hours (or simply not taking pictures during those times of especially rapid light change).
"Should it be 5 seconds?"
Possibly for shooting at night, but 5 seconds will almost certainly be way too long of an exposure for shooting during the day. Again, the specific choice of exposure time needs to be dictated by the actual conditions you're in when you're shooting the timelapse... Any answer to this question given here will be pure speculation at best.
"Should I take more pictures than 5760 over the entire length of the trip?"
Given the variables that you've provided...
Yes. If you can take more pictures, you almost certainly should take more pictures. My recommendation is to take as many pictures as you possibly can. In other words, work in manual mode, set your shutter, f-stop and iso, then simply have your intervalometer fire frames as fast as your camera can go.
The reason for this is that it is extremely easy to speed your timelapse up (by simply removing a given number of frames in post) if you need to, but it is nearly impossible to slow a timelapse down in post (because there are no extra frames to add).
Now this assumes that:
- You don't care about shutter actuations (And you shouldn't. Folks who worry about that are almost always being penny-wise and pound foolish with a part of their camera that can be replaced for about $200... Depending on the shutters expected total number of actuations this is between .004 cents and .00006 cents per actuation. Cheap!)
- You have enough storage space (External large terabite drives can be purchased for under $100... This shouldn't be an issue)
- You are in a position where you can dump your frames directly to your computer in realtime as the trip unfolds (Because you probably don't want to be frequently stopping in order to dump cards to your computer)
If the above assumptions aren't true, then it becomes very easy to calculate for the total number of actuations that you want to 'spend,' and/or your total amount of HD space, and/or the number of times you want to stop to 'manage' your cards.