Botany Manor

To grow the Fool's Emerald you will need to do the following:

1. Fill a pot with soil
2. Add the Fool's Emerald seed
3. Water the seed
4. Fill the pool with water by finding the missing crank near the broken lawnmower
5. Move the potted seedling into the now-accessible cave
6. Get the telegraph machine from underneath the boathouse and place it on the table, in the cave, next to the seedling
7. Open the telegraph machine and input the morse code for the letters K and A, in that order

Chapter 5

To grow Fool's Emerald: Grab the handle near the pond and put it back in the grotto to fill it with water. Fill the pot with soil, add the seed, and water it. Place the pot in the cave across the pool you created. Grab the telegraph from under the boathouse and place it in the cave. Now put in the following Morse Code:
DASH - DOT - DASH - DOT - DASH


Full video walkthrough including all achievements, puzzle solutions, and collectible locations! (Timestamps in YouTube Description)

this actually requires you to get the Frogger achievement before you can get this one so for convenience i begin this guide with my guide for that achievement (list item number 1 below) and then move into how to get this achievement after that one is completed:

1. once you have access to the Formal Garden at the start of chapter 5, if you look to the right of the gate that leads to the boathouse (towards the bottom of the area past the pergola and the already existing pond) you will see an old pushing lawnmower with a white handle beside it.. pick up this handle and take it back up to the white pedestal in between the two staircases.. once you place the handle on the pedestal in the correct spot on the top, the Frogger achievement will pop after the water fills the empty pond and lily pads form on it
2. from here, go up either one of the stairs to collect the Fool's Emerald seeds
3. fill a pot with soil at one of the plant worktables
4. add an Fool's Emerald seed to the pot
5. water the seed
6. take the seedling into the cave you gained access to after bringing the handle back to the pedestal above
7. go back to the area the boathouse is in and when you first enter that area you can go to the right underneath the boathouse to pick up the telegraph machine which you can then transport back to the cave (set it right beside the flower)
8. open the telegraph machine and input the morse code for the letter K followed by the letter A (dash dot dash dot dash is the correct sequence and then the achievement unlocks when plant is done growing)

be careful because @confusedgeek said that he quit out of the game while he was holding the telegraph and it disappeared from his game

As there is other guides before this please see them first.

Chapter 5
You will grow this plant in chapter 5 after filling the pond between the 2 sets of steps at the first garden.

1.Find the lever in the lower garden just outside the boat house gate, it will be next to the lawnmower
2.Bring the lever up to the first garden and add it to the pedestal right in front of the empty pond/water feature and it will fill up with water and leaves
3.Now fill a pot with soil
4.Add Fool's Emerald seed
5.Add water
6.Take the plant into the cave where you just filled up the water, just walk along the leaves to get across the water; place the plant on it's spot
7.Go into the boat house area and as you face the potting table outside, head to the right just under the bridge to find the telegraph, pick it up and take it back to the cave next to the plant
8.Open the telegraph and enter the morse code:
Dash Dot Dash Dot Dash
9.If done correctly the plant will now grow

If you need more help with this you can see my video below: