South Korea will next play China in Shenzhen next Tuesday, while Singapore host Thailand the same day.
"A huge compliment to the team, a very professional performance," Klinsmann said.
"Five-nil is a nice scoreline to read but it doesn't really show you the energy and effort you have to invest in order to get to that score line."
The Koreans dominated possession at Seoul World Cup Stadium but they had nothing to show for it until Cho Gue-sung struck in the 44th minute.
Paris Saint-Germain midfielder Lee Kang-in sent a curling cross into the box and FC Midtjylland forward Cho caught the visiting defenders napping to sneak in behind and slot the ball home.
Cho had struck the crossbar with a volley on 34 minutes, one of several opportunities that South Korea failed to convert in the opening half. The hosts also had a goal ruled out for offside on 21 minutes.
Four minutes after the restart it was 2-0 when Hwang Hee-chan of Wolverhampton Wanderers headed home for his second goal in as many matches for his country.
After Singapore had a goal chalked off for offside, skipper and talisman Son made it three with a delicious left-footed curler from outside the box just after the hour.
Hwang Ui-jo of Norwich City scored a penalty to make it four and PSG's Lee put the finishing touch on an easy victory with a left-footed strike on 85 minutes.
"We needed to have patience," said Klinsmann.
"It's very, very difficult to play teams like Singapore who basically come, first of all, to defend with two blocks of five, so pretty much 10 players in front of their goal."
