We've done that a bit. I would recommend using a corrugated plastic extension from the aluminum gutter which ties into an "above ground" 5" PVC sewer line, OR, more corrugated tubing.
We made the mistake of using a one piece corrugated tubing from the downspout to about 15' away popup outlet.
Well, the corrugated tubing above ground has popped a crack (maybe because my dogs) and now, the only way I can replace is to replace the entire length of corrugated tubing.