Yes, this is normal. vCenter 6.5 cannot manage ESXi hosts below v5.5.
Then, an upgrade from 5.1 to 5.5 U3 can be a solution ?
It's an ESXi 5.1.0799733 standard
If possible to upgrade, then, is it mandatory to stop and to move all the VMs to another server, before upgrade ?
Yes, you can upgrade from 5.1 => 5.5. Yes, you will have to stop and move and VMs off the 5.1 host before you proceed with the upgrade.
Yes you are correct.
You can upgrade and have all VM's moved before you upgrade .
Please mark this as "correct" or " Helpfull" if this answers your query.