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.
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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