Hey there, A Furry Peanut!
I'm afraid that an external HDD won't get the job done. Besides, even if the HDD has 5,400 RPM, it's actually limited to the transfer rate of a USB 3.0 port.
I believe the best storage solution for a gameplay recording in your case would be to use an internal SATA HDD that incorporates 7,200 RPM. A hard drive with such capabilities would be able to withstand the demanding performance for a great recording at 1080p 60 fps.
Good luck!
SuperSoph_WD