First convert the fractions so they have the same denominator so they can be comparable.
The common denominator is the least common multiple of 3 and 5 is 15.
To convert 2/5 to have a denominator of 15 multiple top and bottom by 3 to get 6/15
To convert 2/3 to have a denominator of 15 multiple top and bottom by 5 to get 10/15
So he had complete 6/15 of the journey by 3 pm and 10/15 by 5 pm.
Subtracting, he completed 10/15 - 6/15 = 4/15 of the journey in 2 hours (from 3 pm to 5 pm).
Which means he completes half of that or 2/15 of the journey per hour.
Going backward from 3 pm, where he completed 6/15 of his journey, he will have completed 4/15 of his journey at 2 pm, 2/15 at 1 pm and 0 at 12 pm, so he started at 12 pm.
Going forward from 5 pm, where he complete 10/15 of his journey, he will have completed 12/15 of his journey at 6 pm, 14/15 at 7 pm. If he completes 2/15 of his journey every hour, he completes 1/15 of his journey every half hour, so he will complete 15/15 (or all) of his journey by 7:30 pm.
