The correct answer to this open question is the following.
Could a modern president run a government with five cabinet members as Goerge Washington did?
No, of course not. It would be impossible. The reason is that times have changed, the number of people has dramatically increased, necessities are different, and we are living in a completely different world that needs specializations for different areas.
Does a president today need 15 cabinet members?
Yes, probably more, because I have mentioned above, the government faces different responsibilities and conditions that required the specialization of different cabinet members. Internal affairs, the economy of the US, US Politics, social issues are more diverse and complicated than before. Foreign relations are also a critical issue that requires the focus and attention of experts that did not exist in the past.