This guide may be usefull to help you plan: Upgrading / Migrating from vSphere 5.x to 6.x (6.5 , 6.7) best practices & Approach – Siva Sankar Blogs
I did some research and it looks that esxi 7 can run version 9 VM. (VMware Knowledge Base )
What I would do if I were you, since there is a new platform, do a testing of the process. Create a test VM in your 5.1 and then move it to your new platform, perform hw update and tools update and see how it goes.
At present VMware only supports 6.5 and later.
So better install/deploy a VCSA 7.0 directly as you have only 3 ESXi's .
Make sure to check all the hardware for support on 7.0 . VMware Compatibility Guide - System Search
ESXi upgrade path ESXi 5.1 > 6.0 U2 > 6.5/6.7 > 7.0 . Quite a long one .
Simultaneously update the VM hardware versions to the ESXi versions to which you upgrade .
Moderator: Thread moved to the vSphere Upgrade & Install area.
First of all, please make sure your hardware/firmware versions support esxi 7.0