It is definitely not the correct part for your Area-51 R2, so I would be leery. Even if you got lucky and the wiring connection worked, the mounting mechanism may be designed for another system. What does the rest of the AIO cooler look like?

The older Aurora 7pin (or Area-51 R1 5pin) black connect can fit on a 4pin fan header (pic) such that pins 1-3 make contact, pin 4 empty, & pins 5,6,7 hang over the header unused / un-needed

On a side note, given that the cooling tubes between the pump & radiator are slightly permeable we can expect a small loss of coolant from the 'closed' system due to slow coolant evaporation = slight reduction in cooling performance over time (even on a new never used but now 'vintage' cooler), & so as the R2 desktop & spare parts for it turn 10years old next year, I do advise by now to move to a newer NVDDX or TFGHM style cooler as the better / best cooler choice (when the price is right)

'The mounting bracket for the CPU that came with the new one does *NOT* line up with the holes on my CPU socket...so I cannot fasten that part down regardless"

The R2 mthrbrd is socket 2011-V3, so u need a 2011-V3 compatible retention ring which is found on your R2 cooler,  so you'd take the retention ring off of the old R2 cooler & transfer it onto any new cooler u buy, if/when the new cooler's ring isn't a match, try your R2 ring & report back, however the advice is to return/exchange/partial refund etc that older-style Aurora cooler anyways if possible

Note: that new Aurora alien cooler WILL fit & was used on the Aurora R4 socket 2011 mthrbrd so long as a 2011 (2011-V3) retention ring was used, so we KNOW the pump housing itself is okay for use over an R2 mthrbrd cpu socket, given the 2011 & 2011-V3 rings are the same, in fact that Aurora cooler can be used on any motherboard released the past 10-15 years so long as the correct socket ring for it is being used

Part# R5TNT apparently shows up in the Dell Parts data-base as an Aurora + Area-51 R1 part, the seller may not have known an R1 & R2 weren't the same ...

Thanks for the info and also for providing what the *correct* alternative part numbers should be.  I've sent an email back to the supplier informing them what they sent doesn't work/fit.  We'll see where it goes from there, but hopefully they have the correct part or I can get a refund.  Appreciate y'all!

You should consider the recommendation made be Cass-Ole.

Here is a full side-by-side shot of both units (sorry it's kind of a bad pic):

The fan/radiator portion of the new part seems spot on with the old one.  Aside from the CPU plug the main differences seem to be that the part that sits on top of the CPU is much taller on the new one.  The hoses on the new one are sort of corrugated-like and more plasticy than the smoothish more rubbery tubes on my old one.

I did also check further though and I can't get this new one to work.  The mounting bracket for the CPU that came with the new one does *NOT* line up with the holes on my CPU socket...so I cannot fasten that part down regardless.

Bleh....now to see if I can get my money back or see if they have the "correct" part to send.

You're a wealth of info Cass-Ole.  So I had already played around with using the retention ring from my old computer.  It sort of seemed like it would work, but I wasn't sure because it doesn't seem to "fully" fit.  The retention ring from my old system is 2 pieces:

When placed on the old cooler, the plastic ring on the right "clips into" the metal bracket on the left.  On the new cooler, the little notches that go around the outisde edge of the cooler are like twice as tall as the ones on my old one and when the metal bracket is positioned onto the new cooler, the plastic ring cannot clip into it (it can't reach high enough if that makes sense).  The notches on the inside of the metal ring with the screws, however, do fit into the notches going around the outside of the new cooler so I don't know if the plastic bottom ring is still fully necessary or not.

Just for some extra context.  This old Area 51 is not my "main computer".  I replaced it not super long ago with an Aurora R12 which is still running well (despite one of the fans on my RTX 3080 making a lot of racket...but I won't get into that lol).  I use this old Area 51 as a Plex server.  It just doesn't really run well anymore due to what I believe is the CPU over heating.  I can boot the system and load into Windows.  Everything runs fine for anywhere from 5-20 minutes depending on load...until every thing starts to bog way down, runs super slow...and then the whole system will just suddenly power off.  I've run all the hardware diags in ePSA and everything passes, but as mentioned earlier, even when I'm just booted into the bios from a cold boot the bios screen header shows the CPU temp at 90+ after only being one for a couple of minutes...which just seems WAY too hot (pretty sure it sitting at idle it should be like half that temp).  Hence why I believe the current cooler isn't functioning as it should.  I just want to get this thing back to a stable state.  If what this place sent could still work despite not being 100% the correct part...I'd probably be game to give it a go, but I'm sure that isn't the smart decision none the less.

The new cooler does indeed have the protective cap.  Its funny because I actually said pretty much the same thing to my wife when I was telling her about all of this in that *IF* I do try to put this Aurora cooler in and see if it runs alright, I'm sure it would be considered "un-returnable" at that point due to the fact that the paste will get messed up once I do, heh.  I'll admit I'm tempted to try it, but I am going to wait and see what the seller responds to me with before making any decisions.  I checked their website and they do show to have the TFGHM Threadripper cooler in stock you previously mentioned....it's just nearly 3X what I paid for this one (bleh).  No idea when I'll hear back from them but I'm going to hold off any experiments until I see what they say they're willing to do here.

You have indeed given wonderful advice and I appreciate all the info thus far.  I've learned quite a bit!

The plastic ring that clips from the bottom (right item in your pic) isn't necessary, it's more for ease-of-use in keeping the metal ring stationary when mounting, without it u just take more care when install occurs

Your new cooler had the protective see-through cap on it which keeps the thermal paste pristine, so if u remove it & try to install new cooler I wonder how the seller will respond to that, but, in the end, that cooler will work in tandem w/your R2 retention ring; it's ok if u need a cooler in a pinch & just want to install & get on w/your troubleshooting session to get an answer over whether old cooler was bad or not etc ... I have no issue here buying/.using someone's used cooler so u may keep an eye out for a cheap used one to hold back as a spare; otherwise I feel I gave the advice u needed earlier on how why & what to buy in lieu of the Aurora cooler u received & was discussed tonight

Would be nice if u can troubleshoot with it tonight & return/exchange it tmrrw ... (=