Combine heavy cream, whole milk, granulated sugar, and salt in a saucepan. Heat on medium-low until the sugar dissolves, about 5 minutes.

In a separate bowl, whisk the 5 egg yolks until well blended. Slowly drizzle in about 1/2 cup of the warm milk mixture while whisking continuously to temper the eggs.

Pour the tempered egg mixture back into the saucepan. Continue heating on medium-low and stir constantly until the custard thickens enough to coat the back of a spoon. Be careful not to let it boil.

Strain the hot custard through a fine mesh sieve into a bowl to remove any lumps. Mix in the vanilla extract. Allow it to cool to room temperature, then cover and refrigerate for at least 3 hours until completely chilled.

Pour the chilled custard into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency. For a firmer texture, transfer the churned custard to a container and freeze for an additional 3-4 hours.