First, let's find the gain for each day. The clock gains 5 minutes every 3 days, so the daily gain is 5 divided by 3. By doing this division, we determine that the clock gains approximately 1.67 minutes (1 and 2/3 minutes to be precise) per day.
Now, we want to find out how many minutes the clock will gain in 4 days. To do this, we just multiply the daily gain by 4. When we perform this multiplication, we find that the clock will gain approximately 6.67 minutes in 4 days.
Finally, we want to convert this time from minutes to seconds, because the problem asks for the gain both in minutes and seconds. There are 60 seconds in a minute, so to convert minutes to seconds we just need to multiply the number of minutes by 60. When we multiply 6.67 minutes by 60, we get 400 seconds.
Therefore, the clock will gain approximately 6.67 minutes or 400 seconds in 4 days.