You can run/walk the whole thing if you want as long as you keep a 16:00/mile pace.
BUT...it's only April. Find a training plan, commit to following it, and I bet you'll surprise yourself come race day...er...night. If you can run 5 miles now you can definitely run 10 in a few months, as long as you train.
You say you really want to "experience" the course, so make it your goal to be well-enough prepared that you can fully soak in everything and not spend the entire 10 miles worrying about whether you'll be swept (because they DO sweep)/finish/make it out alive.
Jeff Galloway is the official runDisney training consultant, and as race day gets closer he'll post training plans. Here's last year's beginner training plan:
http://as1.wdpromedia.com/media/ewwos/pdf/rundisney/Galloway/TOT12beg.pdf
This one might be more your speed since you have some experience running:
http://as1.wdpromedia.com/media/ewwos/pdf/rundisney/Galloway/TOT12fin.pdf
In the meantime, find a local 10K race to run so that you can submit a time to runDisney for corral placement.
Good luck!