Either the tag is dead wrong or what you bought is not a Heather. Yes, they survive in zone 5. They live in Northern Europe.

They like acidic well-draining soil. Pure clay is no good. I'd amend your soil with some peat moss and sand. Make sure it gets sun.

Whoa, I assumed all Heathers were cold-hardy, apparently there are Southern European varieties as well. You will need to research the particular cultivar you bought.
If you purchased it at a local nursery in zone 5 then it SHOULD be a hardy variety; if not return it and complain LOUDLY that they should not be selling zone 9 Heathers when there are so many nice zone 5 Heathers available.

I would return this Heather also if it is not zone hardy here. Before buying any Heath/Heathers you really need to know your soil PH. You can buy a device at the box stores and they are reasonable - around $5. Soil PH will tell you what type you can have. I am typical Ohio with clay soil and neutral soil bordering on alkaline. I can only use certain Heath's here but mine look great and to boot they are on my SW side so lots of sun and open to quite a bit of winter winds. I did not amend my soil. I lost a few the first winter but it's been great since then. Why battle soil amendments forever when you can just buy some that are alkaline tolerant. I got mine online for a source of what I needed.
Cher

There ARE potted heaths sold in floral departments and big box stores usually with colored foil on them that are NOT hardy past zones 9-11.

Erica persoluta hybrids are what they are and they are grown for florist potted color not for landscape plants.

These are very colorful but are meant to be tossed or dried when they are done blooming.

Here is a link that might be useful: florist potted