I am getting the same issue. Our company just received these models and all other models are still functioning under the original Task Sequence. Could any Dell Tech support or knowledgeable person answer this with a possible solution?
I was just fighting the same issue, and on a whim I downloaded the latest winPE cab file from http://en.community.dell.com/techcenter/enterprise-client/w/wiki/11530.winpe-10-driver-pack and it now works. Hope this helps!
I know it's been a while since this was posted, but I was having the same issue as OP and had the WinPE 10 driver pack already loaded in SCCM.
Our 5040 are the small FF and have Intel I219-V NIC. I was trying to PXE boot so I could install a company image (Windows 7) on the workstation, but every time WinPE would load it would reboot because the NIC drivers weren't installing. I verified the NIC driver was added to the boot image several times, triple checked that it was the same driver from Dell's support site, tried a slightly newer driver from Intel's site, even booted in to the OEM version of Windows and checked the drivers - all were the same. I even went as far as putting the drivers on a thumb drive and loading via the command prompt but it just wouldn't work. On a whim I loaded the Windows 10 NIC drivers in to WinPE via USB and command prompt and that worked. I'm guessing this is because I'm using WinPE 10 but I've never had to do this before. The driver I loaded was E1D65x64.inf -- we're using x64, if you're using x32 I believe the driver will be E1D65x32.inf.
I just got done injecting the new driver in to our boot image and I'll test PXE after the local DP is updated.
Forgot to update my post back in May. Your answer is correct. Not long after this I was able to use DISM to inject the correct NIC drivers into my boot images but thanks for letting everyone know. Its too bad Tech Support couldn't provide us with an answer.