It really depends where you live within zone 5. It is considered a banned invasive in Washington state, and often self-sows and spreads in the northwest and similar areas, which have alpine climates.

No problem in the subtropical southeastern USA, which doesn't provide alpine plants with a beneficial environment. The nights are too hot and humid.

In the Midwest and northeastern states, there is persistence and a tendency to self-sow, but in a controllable way.