The card states heal 5 dmg bit not up to 5 dmg so can it be played if you only have 4 dmg on your character?

Yes the 5th healing damage would fizzle.

You do as much of the card as you can.

So what about you have to resolve the first part before triggering the second? Or is that just after the Then key word?

That's just with "then."

It should read, Up to 5 damage. Bad wording is systemic right now at FFG.