I am also in zone 5 (actually 5b NE Ohio). I would go ahead and plant the bulbs. I don't know about the Asiatic lillies as I have never planted those, but I would definitely plant the tulip bulbs as soon as you DO get them.
Most mail order companies will ship plants or bulbs at the right time for planting in your area, not right when you order them. So, the fact that they are shipping them out to you now, means that it is the right time for planting them now.
Good luck with your garden!
I also planted some tulip bulbs. Really neat ones, lilly flowered, and Apricot Impressions Darwin Hybrids.

Ditto what kentstar said.

I would also plant the tulips when you get them (I've planted on New Years day here a few years--months after I should have and all 300 bloomed beautiful). As for the lilies I would also plant them (I'm not sure what other option you would have with a lily bulb).

Good luck
Maureen