In a medium bowl, stir together cracker crumbs, melted butter, and 3 tablespoons sugar. Using the bottom of a measuring cup, press mixture into bottom and up sides of a 9-inch deep-dish pie plate.
Bake until golden, about 10 minutes. Let cool completely.
In the bowl of a stand mixer fitted with the whisk attachment, beat cold cream, vanilla, and remaining 2 tablespoons sugar, gradually increasing mixer speed to medium-high, until stiff peaks form, 2 to 3 minutes. Transfer to a large bowl.
Clean bowl of stand mixer. Using the paddle attachment, beat cream cheese at medium-low speed until smooth, 1 to 2 minutes. Add condensed milk, lime zest and juice, and food coloring (if using). Beat at medium speed until well combined, 2 to 3 minutes, stopping to scrape sides of bowl. Fold in whipped cream mixture. Spoon into prepared crust. Cover with plastic wrap, and refrigerate for at least 4 hours or up to overnight.
Just before serving, spread sweetened whipped cream onto pie, and garnish with thinly sliced limes, if desired.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/key-lime-icebox-pie/