Preheat Your Oven: Adjust your oven rack to the middle position and preheat to 350°F (175°C).
Prepare the Filling: In a large bowl, whisk the 5 egg yolks until they are pale and slightly frothy. Add the can of sweetened condensed milk and whisk until the mixture is smooth and well combined.
Add the Key Lime Juice: Slowly pour in the key lime juice while continuing to whisk. Keep mixing until the filling is smooth, homogenous, and has noticeably thickened. This thickening is the natural chemical reaction that helps the pie set.
Fill the Crust: Pour the filling into your prepared graham cracker crust and use a spatula to spread it into an even layer.
Bake the Pie: Place the pie on a baking sheet for stability. Bake for 15 minutes. The pie is done when the center is set but still has a slight jiggle when you gently nudge the pan. Be careful not to overbake, as this can cause the texture to become rubbery.
Chill Completely: Remove the pie from the oven and let it cool on a wire rack at room temperature for about 30 minutes. Afterward, transfer it to the refrigerator to chill for at least 3-4 hours, or preferably overnight. This chilling period is crucial for the pie to fully set and for the flavors to meld.