I can say from personal experience that I can carry 5 lb. loose on my hip, a 10 lb. sack in my hand, or 12 lb. on my back without any noticeable decrease in mobility or speed. Unless the stones were 1 lb. each, any unarmored slinger could have carried more. On the other hand, it is very foolish to not carry as much as possible. Those two things together seem to point to a less apparent reason for the five stones.
It is no coincidence that Goliath challenged the Israelites for forty days, the rain that caused the great flood lasted for forty days, Noah waited another forty days before opening the ark, and moses was on Mt. Sinai for forty days receiving God's work,
etc. Numbers always have very specific, symbolic meaning in the Bible. Four is the number of man, one is the number of divinity in the Bible, and five is the number of grace. It's one added to four in order to strengthen it. Another instance of this is the changing of Abram's name to Abraham when he was called to walk before God. It's significant because God added the number five (represented by the 5th letter of the hebrew alphabet, hei) to the middle of Abram's name. "Av-ram" became "Av-ra-ha-um." When Jesus (one) fed the crowd on the mountain (four), he did it by giving them five loaves, which represent grace especially well within the context of his feeding people. Add the 2 fish to the five loaves and you get seven, the symbol of perfection, which refers to Jesus being the only prefect man. IMHO, almost every number in the Bible was inserted there to convey a specific meaning and we've lost the cultural context with which to understand a lot of them.
Extra-biblical evidence points to David having been Saul's shield bearer as well as his well known job as a shepherd. Given this, David was likely older than 15 and an adept fighter in his own right. He'd need to be in order to protect himself while weighed down by Saul's equipment and his own. We can also gather that regardless of whether David was good with the sling, we are supposed to think he was. Otherwise he wouldn't have gone into battle with a sling as his primary weapon and there'd be no point in his bragging about killing a lion and a bear while tending his flock.