In a skillet over medium heat, add the olive oil and sausages. Fully cook and brown the sausage. Remove from heat and let cool.
Unwrap the crescent dough. You should be able to make four rectangles with the amount of dough. On a lightly floured surface, gently roll each of the rectangles. Using the short end of the rectangle, place one cooked sausage and roll for one full rotation. Cut the dough and form it around the sausage. Place the dough-wrapped sausage on a lightly greased baking sheet and set aside. Repeat until all sausages are rolled. Use the excess dough to form the last rectangle for the fifth sausage link.
At this point, you can cover the sausages and refrigerate until ready to bake.