How do you get the Season 2015 - 5v5 Diamond?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Diamond in the 2015 ranked season in 5v5 Team Ranked.”
Is the Season 2015 - 5v5 Diamond still available?
No. The Season 2015 - 5v5 Diamond was a ranked reward: to get it you had to reach Diamond in Ranked 5s during Season 5 (2015). Riot does not give out past ranked rewards again, so it cannot be earned anymore.
