Chosen Solution

After I have had for a long time the same “purple speck” issue with the back camera of my old iPhone 5s that other folks around here have reported, I finally got to exchanging the camera with a third party replacement part,  following the corresponding ifixit.com guide, minutely. At the same time, I also replaced the battery, I should let you know. Result  of the whole operation: (New) back camera doesn’t work (shows black screen). Plus: camera gets extremely hot!! You can feel it through the back cover; when turning off the phone and taking out the camera, you can barely touch it, so hot does it get. Put the original, faulty, camera, back in —> works normally, doesn’t get hot at all. Any idea as to what the reason for this issue might be and how it might be solved? Thanks a lot!

Your replacement camera is bad. Solve it by getting a new replacement that isn’t bad.