There are 2 Connect for SharePoint releases for EPiServer 5:
Connect for SharePoint 1.0 for EPiServer 5 SP1, it allows to push SharePoint content to EPiServer CMS through content channel. SharePoint 2007 and WSS 3.0 are supported.
Connect for SharePoint 2.0 for EPiServer 5 R2, it allow to push SharePoint content to EPiServer CMS through content channel and includes VPP that allows to access SharePoint files from CMS site. SharePoint 2007 and WSS 3.0 are supported.
Latest release of Connect for SharePoint 7 allows pushing SharePoint content to EPiServer CMS 7 and also includes a VPP to access SharePoint libraries from CMS side. It supports SharePoint Server/Foundation 2007/2010/2013 and WSS 3.0
This version contains solution file that can be installed on SharePoint Server/Foundation 2013 and contains number of bug fixes and additional features comparing to first releases, please see Release Notes.
You may try to install 2 solutions: Connect for SharePoint 2.0 on EPiServer CMS 5 R2 and Connect for SharePoint 7 solution on SharePoint 2013. It may work, since the same content channel feature is used to push SharePoint content to CMS. However, I don't think that this combination has ever been tested and I'm not sure if it is officially supported.
Is it possible to use EPiServer Connect for SharePoint (any version) with EPiServer CMS 5 and SharePoint 2013?
And if it's possible, are there any limitations compared to when using the connector with EPiServer 7 and SharePoint 2013?