You could use an RC circuit network, but you'd still have to have it driving a Transistor that's Emitter-Ground, as the line's active low. Also, RC Circuits make my head hurt, I don't understand analog quite that well.
Easy way would be using two 555's or a 556 (555x2!), one in Monostable, one in Astable, and set up the timing for 5 pulses to come across in say.. 20ms or so (You'd have to mess with the timing!). Ok, so, not real easy, but cheap! Probably just a couple of bucks. You'd also have the issue if you hit the thing back to back, if the ramp is too sharp, you run the risk of restarting the Monostable 555 in the middle of it's operation, so you'd end up with some number less then 5 pulses, possibly.
Personally? I'd spend the $25 and use an Arduino or clone (Pro Mini, 5v), and set that one up to drive a Transistor for your pulses. That way, you can have the Arduino buffer it's pulse count, so that even if you stack balls back to back, it'll just keep pulsing till it's emptied it's buffer.