The problem with choosing to print on A5, rather than A4, is often that A5 paper seems to cost more than A4! (I assume that it's simply because it doesn't sell anywhere near as well as A4 does).
However as long as you've got some A5 paper (either because you managed to buy it at a reasonable price or because you've bought A4 and cut it in half) then, of course you can print on it. (The same applies to any other paper that will physically fit into your printer).
First, you need to load the paper into your printer. Some printers only have one place to put paper into, whereas others offer you a choice (so that, for example, you can have both A4 and A5 paper available for use at any one time). Put the paper into wherever is most convenient and adjust the edge guides so that it's a snug fit.
Produce your masterpiece as usual and then go to File > Print (or press Ctrl and P together), just as you normally would. Then - here's the important bit - click on 'Properties'. You'll then see lots of options, which allow you to tell the printer what type of paper you've inserted, which way round it is, what size it is, etc. (If you've got more than one place to insert paper, you can also tell your printer where you want it to draw the paper from).
Once everything is to your liking, click on OK. Then click on OK again to start printing.