For zone 5 I don't think there is much of an option besides making some kind of greenhouse. I just brought my container herbs inside for the winter. Even inside, some herbs won't last.

chives - Hardy in zone 5, leave planted in ground outside
genovese basil - annual
dill - annual
sage (noid) - which sage? Hardiness depends upon variety. I'll assume S. offinalis. Hardy in zone 5 with good soil drainage.
parsley - biennial. Hardy, though.
thyme - again which thyme? Hardiness varies. I'll assume T. vulgaris. Hardy in zone 5 with good soil drainage.
margarita mint - Google the various fancy mints. I'm not positive on their zones.
kentucky colonel mint
ginger mint
grapefruit mint
hazelnut latte mint
black pearl peppers - tender plant. Peppers are annuals in northern zones.
big bertha bellpepper - ibid.

FataMorgana

Peppers are annuals in northern zones.

I have a friend who overwinters peppers indoors, then puts them back in the garden the next year. She says they do great. I imagine you'd need a very sunny window, however.

Yes, I've heard of people doing that as well. Given the pepper's love of heat and sun, I expect few people will have the conditions to overwinter their peppers well.

It doesn't hurt to try, if the OP wishes.

FataMorgana