That pattern is called short cycling, and it usually points to the pressure tank rather than the pump itself. A waterlogged tank, one that has lost its air cushion, forces the pump to turn on and off far more often than it should.
A failing pressure switch is the other common cause, either sticking in a way that keeps triggering the pump or losing its calibration so it no longer matches the tank’s actual pressure range.
The pump itself failing outright usually shows up differently, as a steady loss of pressure across the whole house rather than a cycling pattern, and that distinction is most of the initial diagnosis.
Age plays a role too. A pump that has run reliably for a decade or more, then starts showing any of these symptoms together, is worth evaluating as a whole system rather than chasing one part at a time.