Yes. The lower the number of the zone, the colder the zone. So usually the gardener is looking at the cold hardiness of the plant. If the plant is hardy to zone 3, it will take colder weather than your zone 5.
having said that, sometimes, the plant really likes cold weather and won't take a warmer zone (a higher zone number indicates a warmer clime). For example, I'm from New Orleans and we can't really grow lilacs and peonies becoz our zone is too hot! zone 9.