Sloth made his AGF senior debut in the Danish Superliga championship on 7 December 2009, aged 17.

[2] In 2008, former teammate Benny Feilhaber proclaimed Sloth as 'the greatest current talent in Danish football'.

Sloth joined Football League Championship side Leeds United on 25 August 2014 on a three-year deal.

[16] On 21 May 2019, it was announced that Sloth had signed a two-year deal with Scottish Premiership side Motherwell, with the move due to be completed in June.

[17] He left the club on 31 January 2020, his contract being cancelled by mutual consent, having only played once as a substitute in the Scottish League Cup.

[20] On 29 October 2020 it was confirmed, that Sloth had returned to Denmark and signed with Danish 1st Division club FC Helsingør for the rest of the year.