To a large bowl, add the beef, peppers, lime juice, taco seasoning, and hot sauce. Use your hands to work the ingredients into an even mixture. Be careful not to over-mix.
Divide the mixture into 5 even balls. Pat together between your palms to form an even burger patty.
Preheat a grill to medium-high heat, about 550°F. When the temperature is reached, add the patties to the grill. Close the lid and let cook for 4 to 5 minutes. Flip and repeat. If the burger does not loosen from the grill grate easily, let cook a few more seconds before trying to flip.
Add the cheese slices to the top of the burgers, close the lid, and let melt for 30 to 60 seconds.
Transfer the burgers to a plate and let rest 5 minutes before serving.
For the Mexican ketchup, mix the sour cream, salsa, ketchup and lime juice in a small bowl. Use as a dipping sauce or topping for the burgers.