Melt 5 tablespoons of butter in a small saucepan. Meanwhile, mix the graham-cracker crumbs with 1/4 cup sugar in a medium bowl. Stir in melted butter until the crumbs are moist.
Tip the mixture into a 9-inch springform pan and press it firmly, creating a 1/2-inch crust up the sides of the pan.
Bake for about 12 to 15 minutes until set, then transfer to a wire rack.
Lower the oven to 275 degrees. Beat the cream cheese until smooth with an electric mixer and slowly add the rest of the sugar. Scrape in the vanilla seeds and beat for a few minutes until thoroughly combined.
One at a time, drizzle in the eggs, scraping down the bowl after each addition. Finally beat in the sour cream and salt and pour the batter into the prepared crust.
Bake for around 1 3/4 hours, until the sides of the cheesecake are set but the center appears soft. Place the pan on a wire rack to cool. Run a knife around the outside of crust to loosen it from the pan.
When the cheesecake is cool, cover it tightly with plastic wrap and leave it to set for at least 4 hours or preferably overnight.