No, the Firenze Card is only available for 72 hours.
If you're here longer and want to enjoy visits to the museums at a more leisurely pace (which I would highly recommend), I'd suggest you instead get the "Amici degli Uffizi" card (you can purchase it at the Uffizi museum, at Gate 2, at their Welcome desk to the left side of the door). It doesn't include as many museums as the Firenze Card but it includes the most popular - the Uffizi and Accademia - and it has a family formula as well as being valid until the 31st of December. If you want to visit other museums, you can just pay the ones you decide you really want to visit.