Haken and Between the Buried and Me come pretty close, but I can't quite definitively say 5 or more songs from one album.
For Haken, it's The Mountain. (Atlas Stone, Falling Back to Earth, Pareidolia, and Somebody. Cockroach King might make my Top 10 Haken songs as well, but there's a lot of competition.)
For BTBAM, it's The Parallax II: Future Sequence. (Telos, Bloom, Melting City, and Silent Flight Parliament. Lay Your Ghosts to Rest and Extremophile Elite aren't too far from my Top 10 BTBAM songs, either.)