According to Official Guinness Records,
The most Rubik's Cubes solved whilst running 5 km is 40, and was achieved by Jeremy Duehring (USA) in Arlington, Virginia, USA, on 28 April 2018. Jeremy attempted this record because he wanted to try something that would combine his love of running and solving Rubik's Cubes.
For a complete list of 2018 records, please visit 2018 Guinness Records in United States.