Turk handily defeated three other candidates Tuesday to capture the GOP nomination.
Turk was the GOP nominee against Cleaver in 2006, 2008 and 2010. After losing by wide margins to the Democrat and former Kansas City mayor in his first two tries, Turk lost by just a nine-point margin in 2010, suggesting Cleaver was weaker than assumed in the usually Democratic district.
This time Turk will face Cleaver in a redrawn district, which now stretches into central Missouri.
Libertarian Randy Langkraehr ran unopposed in the 5th District primary.
One of the most closely watched House races in the country this November will be Missouri's 4th Congressional District, where U.S. Rep. Vicky Hartzler, a Republican in her first term, will face Cass County Prosecutor Teresa Hensley.
Hensley was unopposed in her Democratic primary, while Hartzler faced token opposition Tuesday.
Like the 5th District, the 4th was redrawn in 2012 to take in slightly more urban voters. But agriculture and defense issues remain the district's primary focus.
Hartzler defeated longtime incumbent Ike Skelton, a Democrat, in 2010.
In Missouri's 6th Congressional District -- which now stretches from Kansas to Illinois along the state's northern border -- U.S. Rep. Sam Graves, a Republican, won an easy primary victory. He is likely to face Democrat Kyle Yarber and Libertarian Russ Lee Monchil in November.
In St. Louis, U.S. Rep. William Lacy Clay defeated fellow Democrat U.S. Rep. Russ Carnahan in the 1st Congressional District race.
The two House members were forced to run against each other following redistricting.
Republican Robyn Hamlin and Libertarian Robb Cunningham are also expected to be on the 1st District's November ballot.