Are they getting at least half a day of sunshine?

Yes they are in the sun all day.

That sounds strange. Do they get plenty of water? They are heavy feeders- you may want to try to fertilize them.
Renee

Ok, I found this from the link below:
"Put the rhizomes about an inch into the ground and space them about a foot to a foot and one-half feet apart. Since they multiply, one this year likely produces two or three in the next year. Over a couple of years a clump will form. If it grows too tightly bound, the blooms diminish. "

Might they have been planted too close initially, thus by the second year they were already a bit tightly bound?
Since it has now been 5 years, I imagine they would benefit from being dug, divided, and reset with the appropriate spacing so they won't get too crowded too soon.

Here is a link that might be useful: Culture of Louisiana Irises