correct count is FOUR (IV).
The war against the USSR was WWIII and it did get hot at times in Korea, Vietnam, and other countries. And was a button push away from thermonuclear destruction in 1983. Who knows how close we came in the 60s with missiles in Cuba etc but a Mutually Assured Destruction attack was almost launched in 1983 by the USSR.
Was that the time when the Soviet general went with his gut and said there was no attack coming from the U.S.?
If it was a world war, it was a continuation of the second, and even with the USSR gone it was continued by Red China.