Why is my volume button stuck?
My dad has an iPhone5 the long version and his volume button (the one to turn the volume down) is not working
Most of the times a button stops working its because it has been pressed too hard. You should hear a small click sound when you press it, if it doesnt click then the contact might be damaged. Inside the iphone there is a contact plate that looks like a small metallic half bubble on a plastic plate. This conducts the electric signal for the volume to go down whenever the bubble is pressed down on the plate, which in turn has a metallic contact that connects to the mainboard.
I would open up the phone and check if the problem is that small contact im telling you about. Im attaching some pics (that i took from iFixit guides btw).
If this is of any help I'm also attaching the links to the parts and the guide that you would need to do the repair.