OK, here's going at it with some actual methodology.
From what I can see, there are nine types with different colours: Action, Treasure, Victory, Curse, Reaction, Duration, Shelter, Ruins, Reserve.
All Knights, Looters and Travellers are Actions, and they don't necessarily bring a lot of extra to the table so we may wish to rule those out immediately. Ruins are all Actions as well but they have their own colour; nonetheless, we will likely get more out of another Action card. So that's one colour we give up on.
Hovel is the best Shelter to take. It gives us two types and colours without using any of the usual primary types.
All Durations are actions. The Durations with the most types are the ones that are also Attacks. So let's take Haunted Woods.
We can take a Reserve. We can grab either Coin of the Realm or Distant Lands. Pre-Empires, there aren't any Victory cards with other types that we can still take, but there are Treasures. So we should take Distant Lands here. (Empires has Castles for another type.)
And then we can take Diadem for our Treasure, and Curse because it's unique.
Total: 10 types and 8 colours in 5 cards.