For me two things come to mind in regard to annuals. Is the growing season where I am long enough for the plants to come to maturity? Is is likely to be successful in my climate? I found a site that said the amaranth in question would mature in 50 days, so I think you have all the time you need to get a successful crop or enjoy it as a decorative accent. Crops that thrive only in hot weather might not be happy in Zone 5, but I am reasonably certain that amaranth is not in this category. Types of amaranth that I have grown did well for me in Zone 6A and even re-seeded.

Thanks for the help Asarum