Hi jtrinid3‌,

This is the validated supported memory for your model:

Alienware Aurora R5 has four DIMM (RAM) slots, which are accessible by removing the left-side cover and rotating the power-supply unit. Your computer supports 4 GB, 8 GB, 16 GB, 32 GB, and 64 GB DDR4 memory of up to 2133 MHz and up to 2400 MHz with XMP (optional).

That Kingston Fury DIMM sounds like a XMP stick, so not really a good match for your existing standard-clocked (non-XMP) 2133mhz Hyundai DIMM.  You should download Aurora-R5 Service Manual now. Something like CPUID CPUz will show better info.
 
A system with only one DIMM can only run in Single-Channel Mode. If you install 2 exactly matching DIMMs, the system's memory will now run in Dual-Channel Mode. That gives you some very good throughput.

So, your best bet would be (in order of preference)

1. Buy another exactly matching Hyundai 16gb DIMM.

2. Replace all memory with 2 exactly matching DIMMs (Eimy gave you specs and it's also in Service Manual).

3. Buy a proper non-XMP 2133mhz DDR4 DIMM from Crucial.com (and hope it will play nice with existing DIMM)

Starting at the main processor, and going left-to-right, the DIMM slots are marked on the motherboard as:

XMM3, XMM1, XMM4, XMM2

If installing only 2 DIMMs, they go in XMM1 and XMM2 ... which are the two white-clipped slots.

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