I sometimes record regions of my screen to demo how things are working. I use CMD+Shift+5 and start recording. Then when I’m finished recording I use CMD+Shift+5 to stop recording. It should save to my Desktop. But it doesn’t seem to unless I start another recording. Then the first recording saves.
Are you stopping the recording after using CMD+Shift+5? There’s a Stop button in the screenshot toolbar to stop the recording or you can click the Stop button on the menu bar.
Have you checked the desired save location from the drop down menu via the Options button? I have ‘Remember Last Selection’ ticked so it will save to another location i.e. my Screenshots folder if I have changed it from Desktop which is the default.