Hi Christine,
As you know momentum ( mass*velocity) is conserved that means that the initial momentum of a system of particles will be equal to the final momentum after some interaction has taken place.
In our problem we have m1=5 kg, m2=15kg v1=3 m/sec and m1*v1=m2*v2 we can solve this equation for v2 which gives v2=m1*v1/m2 =5*3/15=1m/s
So when the two masses collided and the first mass comes to a stop the second mass takes off with a velocity that is in the same direction as the first and whose magnitude is 1 m/s.
Regards
Jim