The allowable out of roundness of the original construction code should be checked first, but will likely be exceeded based on a depth of 5 inches. API-579 has procedures for evaluating dents in Part 12, but those procedures are limited to carbon steel cylinders less than 6.625 to 42 inches in diameter subject only to internal pressure (and other requirements). It is likely that a Level 3 assessment will be required for such a severe dent.
More information would also be helpful such as the shell type (cylinder, elliptical head, etc), dent direction (inward, outward), shell dimensions (thickness, diameter), and code of construction. Also, is the general profile smooth, or is there local metal loss indicative of a gouge?
