Preheat oven to 325° F.
In a medium bowl, whisk together the egg yolks, sugar and vanilla. Set aside.
In a small saucepan over medium heat, warm up the heavy cream. Remove from heat just before it starts to boil.
While whisking the egg yolk mixture, slowly add about 1/4 cup of heavy cream to the mixture (see note on tempering eggs). Once the cream is incorporated, keep adding the remaining cream bit by bit while constantly whisking, until everything is combined.
Place the ramekins into a large baking pan. If the ramekins don't fit into the same baking pan, you can use multiple small baking pans instead. Evenly distribute the custard mixture into the five ramekins. Slowly add about 1/2 of hot water to the pan so that it comes about half way up the sides of the ramekins.
Using oven mitts, carefully transfer the pan into the oven, placing it on the middle oven rack. Bake for about 30-35 minutes, or until the edges are set and the centre is still jiggly but no longer liquid (start monitoring them at the 25 minute mark).
Once the custards are done cooking, remove from the water bath and set them on a cooling rack to cool down. Once they are cooled to room temperature, cover with plastic wrap and put them in the fridge to set for a minimum of 4 hours or overnight.