Take a step back and find out WHAT YOU HAVE TO DELIVER.
What's the playback device? Does it need one file with huge dimensions, or five 1920x1080 files? What media container and codec does this playback device require? Can it transcode to the proper codec as the delivered file or files are ingested into it? What frame rate does the client need?
You need to ask a lot of fundamental questions about the final deliverable product before you begin work in earnest.
There are several codecs that support any resolution but a file that large will have a hard time playing back from a single stream.
As Dave said, your first job is to figure out how they are planning to play back the signage.
The delivery device is a PC. The software and it's supported formats are here.
I believe since he is using this as a single large desktop across 5 screens it will need to be one large file but I haven't located a code that supports that size.