Hmm... Ill do my best here. To use Hedwig's Theme as a reference, you may want to consider Dvorak's Water Goblin (much longer than 4 to 5 mins!), Grieg's In the Hall of the Mountain King (a bit shorter).
Although, the only piece in memory which has both made my soul soar and disturbed me would be Grofé's Cloudburst.
Since you seem to be into the Harry Potter type music, how about looking at the soundtrack from the new movie, Order of the Phoenix?
Lets see here.. A few of my favorites: Professor Umbridge Fireworks Flight of the Order of the Phoenix Another Story (It's a different version of Hedwig's Theme)
Those are less than 4-5 minutes though.