Is it "5–6 weeks are a lot of time" or "5–6 weeks is a lot of time"?

Use is because you're talking about a single period of time with a range-based duration.

There are extensive discussions of the subtleties of Collective Nouns and Mass Nouns on Wikipedia that explain from a technical perspective why some seemingly plural things are treated as singular grammatically.

You use the singular because it's a quantity of time. From this website

Quantities or measurements of time, money, distance, weight usually take singular verbs.

It's not just restricted to time, money, distance and weight;

Fifty milliamps is enough to kill a man.
Three G is enough to make a pilot black out.