In my own personal experience, square frames are usually a little tricky to find in your local department store. The only size I was able to come across was a 10x10 matted frame with a 5x5 opening. Smaller sized ones like 5x5's are pretty much non-existent in my area. So what to do???
The easiest thing to do is to purchase a mat for your photo. In my shop, I have two mat sizes, one of them being an 8x8 mat for 5x5 photos. 8x8 frames seem to be a little easier to come by, and adding a mat simply finishes off the look of a photo. There are also sellers on Etsy who sell square 8x8 frames or may be able to custom make some for you.
No luck with the square frames? You could also always opt for a standard 8x10 mat with a 5x5 opening, as shown below. Hung vertically or horizontally, 8x10 picture frames are very common and super easy to find anywhere. With this option, framing and hanging your square photo is a piece of cake! Check out the Matting Services in my shop!