The first person shakes hands (X- 1) times.

The second person shakes hands (X-2) times, * * shaking hands (X- 1)+(X-2)=2X-3.

etc

The fifth person shakes hands (X-5) times, * * shaking hands (x-1)+(x-2)+(x-3)+(x-4)+(x-5) = 5x-15.

From the meaning of the question: 5X- 15= 15 X=3 (impossible).

The sixth person shakes hands (X-6) times, * * shakes hands (x-1)+(x-2)+(x-3)+(x-4)+(x-5)+(x-6) = 6x-21.

Judging from the meaning of the question: 6X-2 1= 15 X=6.

Six people attended the meeting.