6 hr and 35 mins after 5:40 pm

\(5:40 \space pm\)

Let us add 6 hours first:

\(5:40 \space pm \\ 6: 00 \\ gives \\ \\ 11:40 pm\)

now, we need to add 35 minutes.

To reach 12:00 AM, we need 20 of these.

Hence, 15 is remaining.

Therefore, 12:15 AM is the desired time.