Solution
The PXIe-5110, 5111, 5113, 5114, 5163, 5164, 5170, 5171, and 5172 all support Linux RT, as we added Linux RT support for NI-SCOPE in version 20.7. However, the 5114 is not part of the 5110 device family.
The earliest version of LabVIEW that supports Linux RT is 2019, which we began supporting with NI-SCOPE 20.7. Later versions of NI-SCOPE have gradually dropped support for older versions of LabVIEW.
Before we added Linux RT support, LabVIEW Real-Time support was only available through PharLAP. We never added PharLap support for our Software Designed Instruments (the 5110/11/13, 5163/64, 5170/71/72), but they are supported on Linux RT.