Melt 3 tablespoons butter in a large skillet over medium heat; add beef, and cook 3 minutes on each side or until browned. Remove from skillet; sprinkle with salt and pepper, and let cool. Melt remaining 2 tablespoons butter in skillet; add mushrooms, and sauté 5 minutes. Stir in sherry.
Unfold pastry sheets on a lightly floured surface; roll to 1/8-inch thickness, and cut into fourths. Place 1 fillet in center of each square; top with mushroom mixture. Bring opposite corners of squares together over beef, gently pressing to seal. Place on a baking sheet; brush with egg white.
Bake at 425° on the lowest oven rack for 25 to 30 minutes or until golden.