You'd have an easier time using the equation if you understood where the equation comes from.
The law here ... the major principle to remember, the key, the fundamental truth, the big cookie ... is the fact that momentum is conserved. The total momentum after they join up is the same as the total momentum before they meet.
Momentum of an object is (mass) times (speed).
Now, list all the things you know, before and after the putty meets the ball:
Before: There are two objects.
Mass of putty = 3 kg
Speed of putty = 5m/s
Momentum of putty = 3 x 5 = 15 kg-m/s.
Mass of ball = 5 kg
Speed of ball = zero
Momentum of ball = 5 x 0 = zero
Total momentum of both things = 15 kg-m/s
After: There is only one object, because they stuck together.
Mass of (putty+ball) = (3+5) = 8 kg
Speed of (putty+ball) = we don't know; that's what we have to find
Momentum of (putty+ball) = 8 x (speed)
===================================
We know that the momentum after is equal to the momentum before.
8 x (speed) = 15 kg-m/s
Divide each side by 8 :
Speed = 15 / 8 = 1.875 m/s after they stick together.
