Since this is an older PC and price is not an issue, I would look at a complete new machine in the $2,000 range. With the current deals going on you can get a nice upgrade.

What is your current hardware config?

Before you started putting money into an 6-7 year old computer, I'm thinking you might want to know if it's even worth upgrading.

As for the video-card, you want a smaller one. Obviously, not too long, but also not too tall (so power-supply arm still closes). 

You still need an appropriate power-supply and don't be surprised if it gets hot under max utilization in that small case.

Aurora R5, video card upgrade

Re: best GPU upgrade for my Aurora R5, price not a problem just the best option that can fit (Plug & play ) with my machine

RTX 3080Ti or 3080 is best gpu validated by user 

benchmark of i7-6700k + RTX 3080 Ti

R5 top cpu i7-6700 bottlenecks the 3080Ti, but you still get decent fps.

for plug n play consider Dell oem gpu

Dell OEM MSI GeForce RTX 3080

Part number = 4Y12V
Platforms = Aurora R12/R11/R10
Card dimensions = Length: 267mm, Height: 114mm, Width: 50mm
Maximum Power Consumption = 320W
Power connectors = Two PCIe 8 pin

Dell / Alienware OEM RTX 3080 Ti 12Gb Graphics Card - Dimensions: 267mm x114mm x 50mm.

user report physically a 10.6 inches / 269mm gpu can be installed with a small amount of room to spare, without removing front fan.