A quad truck will have to be quite large to safely handle 5000lbs on the forks plus the weight of the attachment. Keep in mind a turnafork attachment alone will weigh close to 1000lbs, and will move the LMC (distance from axle centerline to heel of fork) a good six inches or so (again based on a capacity of 5000lbs) so with that and a quad lifting all this mess to 240" or even 189" with a triple, youll need a big hefty lift truck. if you want to drive it in the snow on top of that, it will have to be a pneumatic, and then it will be even bigger. and make sure whomever sells this truck to you has properly derated the mast to reflect the attachment!!! If someone bangs on a turnafork with positioner onto a standard 5000lb truck with no sideshift, you'll be tipping it over with half the rated load on the forks!
these are uncommon specs all grouped together like that, so finding a used lift truck with all those features will severely limit your options. how long can you wait? consider leasing a new machine with a maintenance contract; with warranty, guaranteed maintenance and possible tax breaks on a lease you may find your operating costs cheaper and certainly easier to forecast.
you might also want to consider redesigning the handling operations between two different lift trucks so you dont end up with a monster you can't run in your warehouse. what can you sacrifice to get the job done?
I like cascade quad masts and attachments, but have heard good things about bolzoni attachments being cheaper but still reasonably reliable. I have always been partial to toyotas but there are plenty of lower-cost trucks out there that will do the job in a lower volume application.