Why does Canada want to buy the coronavirus vaccine five times its population? Isn't this an injustice to poor countries?

Actually Canada has already announced  they bought that much to help poor countries. Canada will provide vaccine without up front payment to some poorer countries

Right off the top these vaccines require two doses, so it's really only 2.5 times the population (if indeed this is true). But there is a lot of talk right now about wealthier nations hoarding the vaccines so that poorer nations can't get them. Maybe it's time for Haiti and Guatemala to send up whatever bat signal the Bill and Melinda Gates Foundation responds to.

Most countries have pre ordered from several manufacturers worldwide as soon as they started working on it, not knowing which one would be available and fully tested for use........so many countries will have more than they need for their own population

They don't want that much.  They ordered enough for the population from several companies, because they didn't know which, if any, would deliver.

Why do Americans spend so much money on their military when that money could help poor Americans with food, housing and healthcare?

Because Canada will donate the excess to countries that cannot afford it, you dumb a$$.