Relay vibrates by itself
If I understood your question correctly, you mean that when apply a 5 VDC to the coils of the relay it switches too many time for 4 secs and turn back off.
I have encountered the same problem with an over voltage protection circuit, when voltage measured reaches the shutdown predetermined value it oscillates a lot of times for a period of time. I overcome this problem by connecting the input pin of the relay with a capacitor to the ground. it helped by charging the coil with a sufficient voltage for operation. make sure that you choose a capacitor value in the range of 100uF. try this out and tell us how it works.