Question
I live in Zone 5 and am wondering if there are any perennials that I can grow in window flowerboxes. Do you know of any?  

Answer
Sure there are, but we don't usually do it unless you want to dote over them all winter to make sure they don't freeze but still go dormant.

Spring bulbs are a sure thing.  If you grow them in pots and place those in the box, you can remove them at the end of spring and replace with summer flowers.

If you have the sun, you can grow lots of things.  If you don't, you can grow those same things, just in pots, and rotate them -- 2 in the sun, 1 in the box, a week goes by and you refresh.  Believe it or not a LOT of people do it and almost every commercial landscaper does this.

Short Yellow and Pink Alliums last for a month.  Yellow Alyssum is a 3 week bloomer.  Short Dahlias bloom for a good part of the season, starting in a month or so.

That's another problem with Perennials.  They are almost always a short season bloomer.  The show ends early, which is why we pick up the rest of the season (often) with Annuals.  You don't have to do this if you're growing Dahlias, but it's a problem if you have Lychnis or Campanula or Gerberas.  And because the windowbox is shallow, it will not provide adequate protection for over-wintering anything.  Bottom line:  Either grow these in pots and rotate, or stick to Geraniums, Violets, Petunias, or other Annuals.  C'est la vie.