No. Despite the similar names, GDDR5 and DDR5 are different kinds of memory: GDDR5 is graphics memory built for the high bandwidth that graphics cards need, while DDR5 is the fifth generation of standard DDR system memory, the RAM a computer’s main processor uses.
The “G” stands for graphics, and each family numbers its own generations, so GDDR5 is not a graphics version of DDR5. GDDR5 is much older: Micron traces it to 2008, with chip densities from 512Mb to 8Gb and a top data rate of 8 Gb/s per pin. On a typical 256-bit graphics card, that works out to about 256 GB/s of memory bandwidth. Graphics memory has since moved on to GDDR5X, GDDR6, and GDDR6X. DDR5 is the successor to DDR4 for system memory, running at 4,800 to 8,800 MT/s on a lower 1.1-volt supply and adding on-die error correction. Micron also notes that DDR5 modules are physically and electrically incompatible with DDR4 motherboards, so even within the DDR family, generations cannot be mixed.
Source: Micron, “The Demand for Ultra-Bandwidth Solutions” tech brief and Micron, DDR5 DRAM product page
Image: GDDR5 chips on a GeForce GTX 980 Ti by Fritzchens Fritz (cropped by Geni), CC0, via Wikimedia Commons.