Why can't I craft a badge when I have 5 different cards?
You need at least 1 of each card there is for a game (in a given series, assuming there will be more than 1 series per game in the future) to craft a badge.
Examining your profile more carefully:
The cards that are faded out are cards you must also get in order to fully craft a badge. Keep in mind, the amount of drops you can get are roughly half of the amount needed to craft the badge.
You'll have to either trade to get your other cards, or buy one via the Steam Market.