Has GTS been shutdown for 4th and 5th generation?
Yep, all WiFi things (so inluding GTS) from 4th and 5th gen are removed. Official announcement by Nintendo said:
As of May 20, 2014, certain online functionality offered through Nintendo Wi-Fi Connection is no longer accessible. The discontinued services include online play, matchmaking and leaderboards for many Wii, Nintendo DS and Nintendo DSi games. For a comprehensive list of games and services that are affected, please check http://support.nintendo.com/servicesupdate. Users can still play the games in offline mode, which continues to offer a rich game-play experience.
In the list below with affected games there are the following Pokemon games:
- Pokémon Black Version
- Pokémon Black Version 2
- Pokémon Diamond Version
- Pokémon HeartGold Version
- Pokémon Mystery Dungeon: Explorers of Darkness
- Pokémon Mystery Dungeon: Explorers of Sky
- Pokémon Mystery Dungeon: Explorers of Time
- Pokémon Pearl Version
- Pokémon Platinum Version
- Pokémon Ranger: Guardian Signs
- Pokémon Ranger: Shadows of Almia
- Pokémon SoulSilver Version
- Pokémon White Version
- Pokémon White Version 2