Final answer:
The best methodology for an external red team performing a black-box penetration test on a network-based application is to use port scanning to identify open ports and then run vulnerability scanners to discover weaknesses.
Step-by-step explanation:
The best methodology for an external red team to follow when instructed to use a black-box approach for a network-based application penetration test would be to go for option C: Examine the application using a port scanner, then run a vulnerability scanner against open ports looking for known, exploitable weaknesses the application and related services may have. This approach represents a typical methodology for external penetration testing, by first identifying accessible services through port scanning and then assessing those services for known vulnerabilities without any prior knowledge of the system's internals. Alternative methodologies, like protocol analyzers (option A) or social engineering tactics (option D), might also be useful at certain stages of the test but are not as central to the black-box approach as directly probing for vulnerabilities.