Menzies was promoted from deputy controller of features late last year as part of a number of changes at the channel. He is understood to be moving to Dubai to be with his fiancée.
Menzies has built up Five's slate of property shows including the Laurence Llewelyn-Bowen-fronted I Own Britain's Best Home & Garden from Talkback Thames and Red House series Best House on the Street. He also hired Charlie Luxton to front the genre for Five.
Other credits include Whizz Kid Entertainment production Help! I've Got a High Maintenance Wife and Breaking into Tesco by Ricochet.
Menzies reports to Five director of programmes Ben Gale and the broadcaster has started the process of replacing him.
Separately, Five has hired Penny Harris as acting controller of acquisitions, following Vanessa Brookman's departure to BBC Vision.
Harris, who has worked in similar roles for Paramount Comedy and UKTV, took up the position last week. Five is understood to be waiting until chief executive Dawn Airey arrives at the end of October before naming a permanent successor to Brookman.
This will be Airey's second spell at Five, having joined the broadcaster at launch in 1996 as director of programmes, before becoming chief executive in 2000.