Harper, Posey & Cano are automatic.
After that it gets tough as the only logical throw back is Kipnis because you have Cano. Kipnis has upside but why gamble when you have the sure thing and you'll have at least 3 more good years from Cano before you have to worry about his decline years.
Lee is the better pitcher but Greinke is younger. Given you only keep 5 players and given most owners usually keep hitters, I'm gonna assume there will be a lot of pitching available in the draft so I'd take the best of the two (meaning Lee) regardless of their age. Looking at your keepers I think it's safe to assume you'll have another big pitcher or hitter to replace Lee with as a keeper next year.
That leaves Headley & Desmond who both had career years, and both did it at the magic age of 27 when players are supposed to take that next step. Both have displayed good speed in the majors and minors and both have never displayed big power in the minors so the jump in HR's are a suprise for both. This makes both of them a gamble, but if I had to pick one to take a chance on I would choose Ian Desmond just based upon his position. Assuming Cabrera, Longoria, Beltre, Wright and Zimmerman are all kept, you'll still get a decent 3rd baseman with players like Headley, Sandoval, Hanley, A-Rod, Prado or Freese. And you could have a chance at a future 3rd baseman with Lawrie, Frazier, Moustakas, Middlebrooks or Machado.