Good question.

It's true what you say about "Always" and "Saturday Night", but I'd rather stick to albums, not compilations here.

The three must-have albums are "New Jersey", "Keep The Faith", "These Days". There's no way without them. While "Slippery" might not be my favourite album of theirs, it IS their milestone, and it is damn good. It defined their sound, so it'll be in the list too. That leaves the last spot... something from this decade. I haven't heard "The Circle" yet - that might be an option.
Otherwise it might be "Crush" - I really like the album for it diversity and great songs (yes, you heard me). It was a reinvention, and while I wasn't happy with the pop-sound at that time, it still features some of their finest moments in this decade, and it's a bridge between the old and the new BJ. The last album with 5- and 6-minute songs, ad lips and all that stuff. Every song here has its own character, its onw style, its own sound - more than on the following records.
HAND would be an alternative, I'm really fond of it lately, and I learned to like even "Story Of My Life" and "I Am". It has gems like "Last Man Standing", "Novocaine" and "I Want To Be Loved". Definitely not "Bounce" or "Lost Highway".

So, that would be my list:

1. Slippery
2. New Jersey
3. Keep The Faith
4. These Days
5. Crush / (HAND) / The Circle