Digital Ocean is a great company in a brutal, low-margin industry. Based on having run a similar (now mostly defunct) company in the past, I would guess that 80% of their customers are on the $5/mo plan.
That $5/mo has to cover the hardware costs: you're buying expensive physical servers to put the VPSes on, and lots of SSDs too. SSDs have a limited lifetime measured in writes, and some of your customers will leave broken programs running that chew through this precious resource for no reason. If you throttle them, they'll complain.
Then there's the support. Handling a support ticket costs you at least $3 in salary and benefits (remember, your typical customer pays $5/mo), and people will demand that you help them fix their broken MySQL server or whatever. They'll yell and threaten when you tell them that this is outside the scope of what you can do.
And don't forget security. Your customers will install broken-ass Wordpress sites and forget to upgrade them for 5 years. Then a worm sweeps through and now a whole bunch of them have been pwned and are mining cryptocurrency. Those pwned customers are complaining and demanding that you fix it, and the regular customers are also upset because of slowness due to the "noisy neighbor" problem inherent to all VPSes.
Speaking of which, preventing one VPS from hogging all the CPU or disk bandwidth is harder than it looks. The two dominant software platforms are Xen and KVM, and neither gives you great tools for dealing with disk bandwidth. Limiting CPU is much easier, but there's still the problem that you're overselling. Which is fine until half the VPSes on your machine are trying to mine Ethereum.
On the bright side: half your customers will buy the VPS, leave it running, and forget about it for years at a time. That's what makes the $5/mo business model work out.
Anyway, I do hope they can become profitable! They run a much better operation than the incumbents they replaced (slicehost, etc).