An update to this.
I've looked at the system logs (/var/log/syslog) and monitored it as I was starting up ES.
I saw this in the logs:
Feb 19 11:19:03 AZUREMACHINE kernel: [2075710.797219] Call Trace:
Feb 19 11:19:03 AZUREMACHINE kernel: [2075710.797219] ? entry_SYSCALL_64_fastpath+0x33/0xa3
Feb 19 11:19:03 AZUREMACHINE kernel: [2075710.797219] Code: Bad RIP value.
Feb 19 11:19:03 AZUREMACHINE kernel: [2075710.797219] RIP: 0x7fe23c670ae8 RSP: ffffb937c617bf50
Feb 19 11:19:03 AZUREMACHINE kernel: [2075710.797219] CR2: 00007fe23c670ae8
Feb 19 11:19:03 AZUREMACHINE kernel: [2075711.737161] ---[ end trace 9a87081911b79205 ]---
Which lead me to this thread:
I upgraded ES from 5.5.0 to 5.6.7 and it's running now, so the immediate issue is solved. I would however like to get 5.5.0 running on this system as it's meant to be an exact copy of another system on this infrastructure.