I was on the right track. And in case you're wondering, yes I am in an elevated command prompt to do this.
----------------------------------------------------------------
C:\Windows\System32>dism /get-wiminfo /wimfile:h:\driverdl\winre4.wim
Deployment Image Servicing and Management tool
Version: 10.0.22621.2792
Details for image : h:\driverdl\winre4.wim
Index : 1
Name : Microsoft Windows Recovery Environment (amd64)
Description : Microsoft Windows Recover Environment (amd64)
Size : 2,988,444,981 bytes
The operation completed successfully.
C:\Windows\System32>dism /get-wiminfo /wimfile:h:\driverdl\winre5.wim
Deployment Image Servicing and Management tool
Version: 10.0.22621.2792
Details for image : h:\driverdl\winre5.wim
Index : 1
Name : Microsoft Windows Recovery Environment (amd64)
Description : Microsoft Windows Recover Environment (amd64)
Size : 2,752,197,069 bytes
The operation completed successfully.
----------------------------------------------------------------
That 10.0.etc number is the version number of DISM itself, isn't it? This doesn't seem to be displaying version information on the wim file.