Firstly, the fact that you said,
"No old songs" depresses me. Don't be so closed minded, contemporary music stems from the music that went before it.
That being said, there's no such thing as depressing music. Composers and song-writers NEVER write songs with the intention of making people depressed. That's as crazy as the Judas Priest court case where they were accused of telling their fans to kill themselves by implanting subliminal messages in their songs.
Now if you're looking for sad songs, I've got a few for you, but not all are from the last 5 years I'm afraid.
1) "I fall apart" - Rory Gallagher
2) "Babe, I'm gonna leave you" - Led Zeppelin
3) Any song by Byoncé because her whiney voice would make anyone depressed.
4) "While my guitar gently weeps" - The Beatles
5) "Suicide Note" by Pantera
These aren't actually depressing songs, but they're damn good (aside from Byoncé). You should probably open your mind to the past masters of songs.
If you want something that'll melt your face and get you depressed at the same time, listen to Mozart's Requiem. It's a beautifully written piece of music, coupled with tear jerking themes and melodies that'll just melt your face!