It was unclear what criteria, if any, Trump was using to describe the IS operatives as the "five most wanted".
The news comes just after Islamic State militants re-pledged their loyalty to the group's leader Abu Bakr al-Baghdadi last month.
Iraqi agents are holding a top aide to Islamic State leader Abu Bakr al-Baghdadi, and used an app on his mobile phone to lure four commanders from the group into a trap, a security adviser to the Iraqi government said on Thursday.
Trump tweeted about the anti-IS raid Thursday, saying those arrested were the "five most wanted" IS "leaders".
The tweet did not specify when or where the five were captured, nor give any names. They were named as Saddam al-Jammel, Mohamed al-Qadeer, Ismail al-Eithawi, Omar al-Karbouli and Essam al-Zawbai and were shown in yellow prisoner uniforms. The Iraqi air force has carried out several air strikes since past year against Islamic State positions in Syrian territory.
A year ago the Pentagon said that there were "some indicators" that al-Baghdadi was still alive a month after Russian Federation claimed to have killed him in a strike near the Syrian city of Raqqa.
Abadi declared final victory last December over the ultra-hardline group within Iraq.
Islamic State, however, continues to carry out bombings, assassinations and ambushes, and remains active in neighbouring Syria where it has also lost most of its territory.