How to save data from an external disk that died

A little under 4 years ago I bought a Seagate Backup Plus Portable 5 TB external hard drive. It's worked fine for years, but recently it started having problems - it would disconnect and then immediately reconnect randomly. It would vanish from Windows and then a second later Windows would discover it again and present it as a newly connected drive. Being the colossal moron that I am, I didn't do anything about it, like backing up my data. I was busy and I didn't have the disk space. Now I found out the disk is basically dead. I have tried 3 different cables, 2 computers, at least 5 different

Question by Shaggydog on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.