Here is the info for the puzzles you need help with.
Hint for Puzzle 5 (Lightning): It starts with the Chief. A certain amount of leadership is needed here.
Hint for Puzzle 16 --> follow the light!
For straight-out SPOILERS, see below:
Puzzle 5--Weather Dancing--Make sure your fire is lit. You need a Chief, Level 2 of Leadership Tech, and 3 adept farmers. First, drag the chief to the fire. Once he/she is dancing, drag the 3 adept farmers to the fire, so they can join in the dance.
Puzzle 16--The Chief and The Princess--You need to have found all three keys and solved Puzzles 13, 14, 15. Once the three keys have been placed in the door, it will open and reveal a secret room. You will need to drop a villager onto the sun dial until it reaches the far left position. Once a beam of light comes into the room, the Chief and the Princess will appear as ghostly figures. This solves the puzzle. Afterwards, you can drop a villager close to them, and the ghosts will reveal their story.
If you still have trouble solving Puzzle 16, then you might need version 1.00.04. Or wait until the beam of light appears and then move the sun dial to the far left position as a workaround the bug.