According to this, it was 7 as of March 2018. (Most recent info I could find).
The U.S. military is officially fighting wars in seven countries, according to the White House’s latest war report. Known formally as the “Report on the Legal and Policy Frameworks Guiding the United States’ Military Force and Related National Security Operations,” the unclassified portion flags ops in Afghanistan, Iraq, Syria, Yemen, Somalia, Libya, and Niger — all under the banner of the same war authority granted in the 2002 Authorization for the Use of Military Force to fight al-Qaeda-linked militants.
US at war in 7 countries — including Niger; US Army rebuilds Afghan firebases; F-35s to India?; and just a bit more… https://www.defenseone.com/