You are susceptible to a length extension attack if you use sha-512 this way. You should hash twice or use sha-3
That said, I don't really see the point since it's no more secure than just using the long passphrase directly.
a 5 word passphrase isn't automatically more secure than a 5 char password if the words are predictable. interesing paper goes into this[1]. brains are generally bad in coming up with good passphrases (not enough entropy :)).
while my example is certainly very hard to predict I want to rule out an attacker predicting what makes the (nonsensical) passphrase.
https://eprint.iacr.org/2016/246.pdf
Edit: there is also a video to the above paper: https://www.youtube.com/watch?v=6-vrumB0UUw
So to get anything out of doing this is basically just assuming that your attacker won't know (or guess) that you're doing this. Maybe it doesn't hurt, but I wouldn't trust it with a low entropy passphrase. I suppose one use for it would be getting more entropy on sites with low password length requirements, like 10-15 characters max.
Another possible problem is if your computer gets stolen and the `echo xxx | sha512sum` command is in your .bash_history file. To me this seems to add a lot of additional risk.