The Twins will lose leverage every season after this one. It's a lot easier to say "no" to an extension when you have $7M in your pocket than when you only have $2M.
5 years, $50M could be enough to get him to sign. His arbitration awards could go $5M/$10M/$15M - that's 3/$20M so you would be tacking on 2 years $30M. [Edit, That's actually 3 years $30M, 2 more years at $20M seems light] His lack of power and bad knees are going to keep him from getting paid silly money as a free agent.
The Twins were able to get Polanco and Kepler to sign for a lot less than I expected.