Went inside the cave I found, which turned out to be Lost Cave. This cave was very maze-like inside as I had to go in the right directions to get to the end. Getting to the last room was not a problem for me since I knew how this cave worked, but I wanted to get all the items before reaching the end, which was kind of difficult as I've never memorized the path to each item. Took a few wrong turns, but in the end I got everything I needed.
Once I found all the items, I took the right path to the last room of the cave. There, I met a trainer named Selphy who immediately dragged me into a battle. I defeated both of her Persian with my Hitmonlee. After the battle, we left the cave and ended up at Selphy's house at Resort Gorgeous. I then went back to Five Island and worked on hatching the egg I received earlier. It soon hatched into a Togepi.