welcome to GDSE!
For what you need, I would suggest using masks
In order to do this, the workflow that I would suggest is;
Open your file (good start) ;)
Make a new layer (bottom right of the layer panel)
Hit 'U' to access the shape tool - you'll want to select the ellipse tool as below;
Holding SHIFT and dragging your cursor will enable you to make a circle shape. The properties for this circle can be changed in the properties panel, so don't worry if you don't get the right size first time.
So the bit to consider here is the W and H properties, you'll want to change them to make sure that they are the size that you need. (Click the link icon between the pair so that you only have to type the change once). The colour of the circle won't matter as we will be simply using it to make a selection.
So you've already established that you want an extra 5cm on the radius of the circle to make sure that you can cover the sides of the print. I would also suggest adding approx. 3mm bleed to that there are no white patches.
Now, you should have an Ellipse 1 layer and it should be at the dimensions that you have figured out. If you CTRL/CMD + right click on the thumbnail for this layer, it will give you a selection of your ellipse (there'll be marching ants). When this happens, select your background layer in the layers panel and then simply click the mask button (rectangular icon with a circle inside - to the right of fX) at the bottom of the layers panel.
If you turn off your ellipse layer, you should be left with the circular shape of your background image.
Now, right click (or alt + drag) to duplicate that background layer, right click on the mask to delete it and make your next ellipse to start the process again.
Once you have completed this process as many times as you need you should be in a position to start saving out the PDFs of the appropriate layers. Remember to make sure your document is set up as CMYK and about 300ppi.
Also just to make clear, this is how to achieve circles like you asked but with print you might as well print the rectangular/square shape and the physically trim the excess once you've managed to get the kind of frame/mount that you want
Hope this helps!