I need to sand my kitchen floor (315 sq. ft.) down to bare wood and re-polyurethane. I'm thinking that by the time I drive 1/2 hour to the rental center, a 1/2 hour back, and 1/2 hour to set-up and start sanding, I could already be close to done using my hand-held 5" orbital sander. Is there any reason I should not use my hand-held orbital sander? Thanks for your help.

It depends on what you expect out of your work. I can see lot's of problems with inconsistent sanding patterns ..but they don't shout at you with natural finishes. Personally I think it would take a full day and more with the small orbital. They just don't have the power. It's getting down to bare wood that's important.

Plus you'll be noticing mistakes when you go to finer grits.

Some useful tips...

http://www.hardwoodinstaller.com/refinishing/diy.htm

My boss, forty years ago told me that it is not imperative to remove all of the old finish if there will be a natural finish on oak. The new poly will amber (yellow) within a few weeks.
I'm sorry you are in this predicament. You could have re-coated the floor before the finish was worn through to bare wood. With modern finishes that are never waxed it is fairly easy to clean the floor, apply one or two coats in the worn areas and then coat the whole room. The final coat will determine the gloss level, so you go over the whole room on the final coat.
I tell people who have a wood floor in the kitchen that the time to re-coat a floor can be determined when the floor is cleaned well. If the floor looks great when it is still wet from dissolving the dirt and then dries to look dull or dirty, this is the time to plan to apply at least one coat of finish. The color of the floor when re-coated will be the color when the floor is wet. If the finish has worn almost through
there is still finish that has soaked into the grain a little so it can be cleaned up by scrubbing, before another coat of finish is applied. If its to bare wood fibers, it can be cleaned up some, but another coat of finish will soak in as it seals the wood.
When one coat only is applied in this case there will be a less shiny spot where is was worn.
A lot of people wait too long to re-coat their floors so exposed fibers darken.
This is just one of the reasons that I recommend a stain on floors before the coats of finish after sanding to bare wood. The stained floors will help blend in the wear that eventually takes place so when the floor finish is renewed with another coat of finish after it has worn because the figure of the wood when stained has light and dark areas. The soft grain which becomes a little darker than the hard grain areas will become more worn and will be the first to darken, but with the pattern of the figure will not be looking badly. A stained floor can be coated with more wear and still be a nice old floor, that is easy to keep clean.
A natural floor turns yellow with time and the grey areas, if not cleaned very well before re-coating will look almost black when coated. With a yellow background,
the area looks dirty. There is not as much incentive to clean a floor that still looks dirty after cleaning, even when it has a protective coat of finish over it so it doesn't take a lot of work to keep it clean.
Not keeping the floor clean contributes to the finish wearing off. Dirt attracts grit which wears the floor finish rapidly.
Sand to bare wood in the kitchen with the right machines. It's a lot of work.
Contractors have all the right tools to make the work easier. Re-coating may be a homeowner project, but it is a major project to sand a large kitchen to bare wood.
A random orbital sander will take days. Plan on at least two weekends to get to bare wood. Then you can start to finish the floor.
If you start to get worn areas again, use area rugs to protect the worn areas. You can then plan a re-coat after more of the room has worn.

Thanks both for your advice. Unless you recommend otherwise, my plan is to use my 3 amp, hand-held orbital sander to sand around the edges of the kitchen. I will rent a stand-up orbital sander to sand the rest of the kitchen. I read that an orbital sander was the safest bet for DIY. I'm afraid of destroying my floor with a drum sander. Do you agree?

You will need a scraper and file to get the corners. Where you don't remove enough finish the floor will be more yellow.
A square-buff is a safe bet. Don't be in a hurry.
Remember that any scratches you make as you go will need to be taken out with the next paper, When you are done sanding the floor will be smooth.

OK. Thanks. Do you agree that renting an orbital sander instead of a drum sander is the safest way to go for someone who is new at this?

Yes, orbital sanders are less powerful and slower but more forgiving.