Bearded iris do not like wet areas, and need plenty of drainage. Non bearded iris love wet areas. Try Louisianas, Siberians, or Japanese if you are daring. There are other species non bearded types which would grow as well.
If your hydrangea bed is well drained (that is the key) you can plant them even if you water the hydrangea alot.
Check the soil. Is there moss and/or mushrooms? Is the soild damp on a non rainy day? Signs of bad drainage. Is there plenty of sunlight and a light soil mix? signs of good drainage.
One other item I should mention: bearded iris do not like an acidy soil. I think hydrangea might like that, I am not sure. Check your ph and if it is on the low side (5.5 or less that is acid)
Good luck,
Laetitia

As Laetitia mentioned, beardless irises appreciate ample moisture and an acid soil. Bearded irises prefer the opposite. Do you know what type(s) of irises you ordered?

In any event, you should NOT wait any longer to get your irises planted in zone 5. Irises should have AT LEAST 6 weeks to root in before your first hard frost.

Laurie

Thank you so much for the responses. Now I understand the differences between irises! I have a box of bearded irises and I will put them in their own nice, well drained bed this week.