World War III started about 30 seconds after V-J day on August 15, 1945, and has been ongoing.
There has not been a 5 year period where the world has had peace in all nations.
At this time, there are "hot" (armed conflicts) all over the world:


The US has been continually in some sort of military action, somewhere on the earth, since 1945.

Just because bombs aren't dropping here does not mean that there isn't global war, it just means that the never-ending global war is on "simmer" rather than "boil" at this moment.