Heat a large skillet over medium heat and add the ground beef. Cook until browned, about 5-7 minutes. Drain excess fat.
Stir in chili powder, cumin, garlic powder, onion powder, salt, and pepper. Cook for an additional 2-3 minutes. Remove from heat and mix in cheeses.
Lay a tortilla flat, spoon 1/4 of the beef mixture onto the center, fold in sides, and roll tightly. Repeat with remaining tortillas.
Heat 1 inch of vegetable oil in a deep skillet over medium-high heat. Fry chimichangas seam side down for 3-4 minutes on each side until golden brown.
Remove from oil and drain on paper towels. Serve hot with sour cream and salsa.