I installed a trellis wall on my deck for privacy. Next year, I want to plant something in a pot that vines quickly and densely to create a living privacy wall. Any suggestions for Zone 5b?
Almost any plant you choose will be bare in winter.
If you use annuals, they’ll die in winter and be very short in spring. By summer, they’ll look fantastic, but then they’ll overgrow your trellis, and you’ll be constantly trimming them back. Come frost, they’ll be dead again.
Woody perennials will require a lot of pruning, but you’ll get more consistent coverage.
Personally, I’d go with hedera ivy. It’s evergreen and hardy, providing privacy all year round. 
This spot gets full sun, so I think Hedera helix would burn. Otherwise, I really like that option since it’s evergreen and, unlike other vines, it wouldn’t attract too many wasps
I live in the UK, where Hedera helix is native. Let me assure you, it does flower! The bees and butterflies here love it. However, I’m not sure if it would be beneficial for your local pollinators. It’s always best to go with native plants.
Wildlife loves it here! It’s a savior for bees, especially if we have a poor nectar flow in the autumn. However, you definitely don’t want to be trying to extract it.
Confederate jasmine grows like a weed.
This is the only non-native option I’d recommend because it does well in a pot and smells like heaven.
The idea of planting morning glories scares me, though. 
Not in 5b it doesn’t
Trachelospermum jasminoides is a fantastic plant. Another excellent option is one that can withstand temperatures as low as -15°C