I thought Linode's "Nanode" ($5 VM) was several years after DO. I remember wishing Linode had a lower tier option and contemplating moving to DO back when Linode started at $20 for their lowest spec.
Linode then dropped the price in 2014 to $10/month [1], and eventually in 2017 introduced the $5 option [2]. DO was definitely around well before then, but I do recall DO becoming more popular around that time. Because for $5 it was awesome to spin up a VM to test a new app.
[1] https://www.linode.com/blog/linode/11th-linode-birthday-10-l...
[2] https://www.linode.com/blog/linode/high-memory-instances-and...