I don't know how many stores you have, you need to plan an outage for every store. If you upgrade the Central Server, the new corresponding Store Setup need to be installed on every Store.
But 5.5. can also send packages to 5.7 only missing of new features of the Version 5.7
First you must upgrade your 5.5 installation to 5.7 as a normal RES Update and then install the Central Setup.
(5.7 and then the Updates up to 5.7.8, do not forget to upgrade all databases including Concept databases manually if some exist.
and then, you need to upgrade every Store Installation with the 5.7 Store Setup.
but.....do not forget the security, a Backup of the full system will be required before the upgrade. Central Server and Store.
I prefer to create a new VM with Server 2016 or 2019 and RES 5.7, Import the Database, run central setup, run subscription conversion.
Check if everything is working. Are the prices still there etc...
Manually upgrade one store or test environment / if you do a store setup 5.7 the system will be turned off and nobody can work until the setup is finish.