I live in z5 also. I can tell you one thing that grows well in pots, get tall enough (most varieties) and thick enough. Canna. The only downside is that they are not hardy in our zone. So you will either have to repurchase each year, or dig the rhizomes and overwinter them in a cardboard box of peat moss.

Ivy? Morning glories?

A climbing plant on a trellis is a good screen. I've seen planters with them attached. That way even when the plant dies, you have a lattice trellis giving you some privacy.

I can't answer the plant question because I'm in zone 8, but if it's hardy where you are Carolina Jasmine is a great climber, and evergreen. It gets wonderfully fragrant flowers in the spring and has dense foliage the rest of the year.

Climbing hydrangea (Hydrangea anomala) is hardy in zones 4-8. I haven't grown it so I don't have direct experience with it, but I researched it before deciding to plant Star Jasmine on my trellis. It's beautiful and evergreen in some zones, I think.

Here is a link that might be useful: Hydrangea anomala