How do you get the Season 2014 - 5v5 Bronze?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Bronze in the 2014 ranked season in Team Ranked.”
Is the Season 2014 - 5v5 Bronze still available?
No. The Season 2014 - 5v5 Bronze was a ranked reward: to get it you had to reach Bronze in Ranked 5s during Season 4 (2014). Riot does not give out past ranked rewards again, so it cannot be earned anymore.
