Answer :

[tex]First\ person-5\ shakes\ hands\\Second\ person-4\ shakes\ hands\\3-th\ person-3\ shakes\ hands\\4-th\ person-2\ shakes\ hands\\5-th\ person-1\ shakes\ hands\\\\1+2+3+4+5=15\ \ shakes\ hands[/tex]
Scryt
[tex]1+2+3+4+5=15[/tex]
There will be 15 handshakes :)