Those are not the odds that he will improve on the next card. Those are the odds that he will improve on the turn OR the river. Technically, with 5 outs, the odds are 8.4:1 against that you will improve from the flop to the turn, and 8.2:1 that you will improve from turn to river.

These equate to 3.9:1 odds that you will improve on either the turn or the river.

MATH:
Odds of improving from flop to turn= 5cards/47unseen cards= 1/9.4
(1 in 9.4 times= 8.4:1)

Odds of improving from turn to river= 5cards/46unseen cards= 1/9.2
(1 in 9.2 times= 8.2:1)

Odds of improving at all= Odds if improving on flop to turn OR Not improving on turn AND Improving on River

(5/47) + [1-(5/47)] * (5/46)