I like to lager at 34 degrees, but you could definitely do it warmer if you absolutely have to. I lager in the keg, often, though.
I think you're talking about fermentation, though, and not lagering? Lagers ferment in the 48-55 degree range generally, and then are racked to secondary and then lagered near freezing for weeks.
I think it would be hard to ferment a lager in a 5 gallon carboy, though. You might not have room for the krausen. Can you fit a 6.5 gallon bucket or carboy in there?