It looks very much like a double mock orange (Philadelphus), which are very fragrant. If your plant is fragrant then I'd say that's what you have.

No fragrance. My leaves seem a little too rigid for Mock Orange but I must confess I’ve never seen one in person.

Evergreen azalea.

Hmmm..........I think I now agree that it's a double-flowered white azalea. Leaves are veined like azaleas, and not like the Philadelphus that I thought it was.

Wow. Love those double flowers!!

Thanks to all. I've done limited searching and have not found a double white azalea for my zone, but I have found some for zone 6. It is possible that it looks scraggly because it has barely held on all these years through some tough winters. But, I have a feeling it's got to be a variety that is hardier to zone 5. It is very pretty!