What is the ruling on frequent handshaking after the five daily prayers inside or outside the mosque? And what is the evidence for that?

Handshaking is a prescribed Sunnah (definition) upon meeting, as the Prophet, peace and blessings be upon him, said: "Shake hands, for it removes resentment," and "No two Muslims meet and shake hands but they are forgiven before they part." Some scholars, like Al-Izz ibn Abd al-Salam, disliked handshaking after prayers because it was legislated for meeting, and so that common folk would not believe it to be a Sunnah specific to prayer. As for handshaking after leaving the mosque, it falls under the general ruling of handshaking upon meeting.