Volume 5? December 21, 2010.
Volume 6 is coming out on December 20, 2011 in the US.
Note that Volumes 5 and 6 make up the entire of "Season 6".
Basically, Europe (or specifically, Region 2), gets "Volume 5", AFTER the US gets "Volume 6", yeah, basically we're behind.
To clear things up about Volumes vs Seasons:
Volume 1 = Season 1
Volume 2 = Season 2
Volume 3 = Season 3
Volume 4 = Season 4
Volume 5 = Season 6A (Episodes 1 - 13)
Volume 6 = Season 6B (Episodes 14 - 26)
Also, note that Season 5 consists of the four "films", split up into four episodes each, i.e. Bender's Big Score, The Beat with a Billion Backs, Gender's Game and Into the Wild Green Yonder.
Of course this is nowhere near as confusing as that of Family Guy:
In Region 1 (US & Canada):
Volume One = Season 1 and Season 2 -- released April 15, 2003
Volume Two = Season 3 -- released September 9, 2004
Volume Three = Season 4A (Episodes 1 - 13) -- released November 29, 2005
Volume Four = Season 4B (Episodes 14 - 27) -- released November 14, 2006
Volume Five = Season 5A (Episodes 1 - 13) -- released September 18, 2007
Volume Six = Season 5B (Episodes 14 - 18) and Season 6A (Episodes 1 - 7) -- released October 21, 2008
Volume Seven = Season 6B (Episodes 8 - 11) and Season 7A (Episodes 1 - 9) -- released June 16, 2009
Volume Eight = Season 7B (Episodes 10 - 16) and Season 8A (Episodes 1 - 8) -- released June 15, 2010
Volume Nine = Season 8B (TBA), and Season 9A (TBA) -- released December 13, 2011
In Region 2 (UK & Ireland), and Region 4 (Australia & New Zealand),
"Season One" has the entire of Season 1, and the first half of Season 2.
"Season Two" has the reminder of Season 2.
Basically, the "Season One" and "Season Two" DVDs are the equivalent of just "Volume One" in Region 1.
Then after this "Volume x" is released as "Season x+1" in Region 2, possibly with a different arrangements, such as for example, one might have the last 5 episodes of one Season, with the first seven of the next, where as the same set in the other region might have the last 6 and the first 6.
Just to clear things up about the release dates for the Futurama Season/Volume boxsets:
Volume 1:
Region 1 = March 25, 2003
Region 2 = January 28, 2002
Region 4 = November 7, 2002
Volume 2:
Region 1 = August 12, 2003
Region 2 = November 11, 2002
Region 4 = May 13, 2003
Volume 3:
Region 1 = March 9, 2004
Region 2 = June 2, 2003
Region 4 = September 24, 2003
Volume 4:
Region 1 = August 24, 2004
Region 2 = November 24, 2003
Region 4 = February 18, 2004
Volume 5:
Region 1 = December 21, 2010
Region 2 = December 26, 2011
Region 4 = November 30, 2011
Volume 6:
Region 1 = December 20, 2011
Region 2 = TBA
Region 4 = December 21, 2011
Season 6A starts in Summer 2012, and won't finish until about Autumn 2012.
Season 6B starts in Summer 2013, and won't finish until Autumn 2013.
Therefore, Volumes 7 and 8 will not be released until probably late 2012/early 2013, and late 2013/early 2014 respectively.