I'm presuming you mean it's a short story contest; in which case, yes, it is very much possible to write a good story with a five page limit. Also, I'd be glad to proofread it for you.
However, in order to double-space for printed version, you'll have to set MS Word (presuming that's the word processor you're using, since I know you've mentioned it a couple times) so that the lines themselves are double-spaced instead of just hitting the Enter key twice after each new paragraph (The only reason you do it for posting online is because automatic spacing and indenting won't register on forums like PB's).
I have an older version of MS Word I use for writing, but I don't think newer versions have changed too much. You should still have a tab labeled "Format" near the top of the screen somewhere. By clicking on that, you should get a list of options; in order to format the spacing, you'll have to click on "Paragraph." That should open up a window with two tabs, one labeled "Indents and Spacing" that lets you adjust how much new paragraphs are indented and how far your lines are spaced. Under the "Spacing" subheading, there should be a box labeled "Line spacing" that you can use to switch the spacing from Single to Double, which is considered standard for most professional reports and such (since it's easier to read when you actually print things). After that, you also can reset the left-hand indent to a half-inch (or .5" as it should appear in the indenting box); you can just hit the Tab button to indent every new paragraph like normal while writing, but I've found this little trick helpful when doing essays in college because it makes the indent automatic (thus eliminating the need to hit Tab button all the time).