Check status of Veeam services
Get-Service Veeam*
output:
Status   Name               DisplayName
------   ----               -----------
Running  VeeamBackupSvc     Veeam Backup Service
Running  VeeamBrokerSvc     Veeam Broker Service
Running  VeeamCatalogSvc    Veeam Guest Catalog Service
Running  VeeamCloudSvc      Veeam Cloud Connect Service
Running  VeeamDeploySvc     Veeam Installer Service
Running  VeeamMountSvc      Veeam Mount Service
Running  VeeamNFSSvc        Veeam vPower NFS Service
Running  VeeamTapeSvc       Veeam Tape Access Service
Running  VeeamTransportSvc  Veeam Data Mover Service
Before upgrade stop all your Veeam jobs and disable all Veeam services and restart server.
 Set-Service VeeamBackupSvc -StartupType Disabled
 Set-Service VeeamCatalogSvc -StartupType Disabled
 Set-Service VeeamCloudSvc -StartupType Disabled
 Set-Service VeeamDeploySvc -StartupType Disabled
 Set-Service VeeamMountSvc -StartupType Disabled
 Set-Service VeeamNFSSvc -StartupType Disabled
 Set-Service VeeamTapeSvc -StartupType Disabled
 Set-Service VeeamTransportSvc -StartupType Disabled
Once the server is back online run the setup.exe, accept the license and click Next

 
Setup will inform you about detected previous version

 
and recognize that you have already licenced version. If you want to provide new license number just click Browse and add new license file.

Veeam 9.5 require Microsoft System CLR Types for SQL2014 and Management Objects. And if you didnt install it already, it will inform you. You have the option to install it now .. just press Install.

 
once installed  you can click Next and continue with upgrade.
Choose under which account will be your Veeam Backup & Replication service running.

Choose a database instance. I am using local MSSQLDB.

Setup will ask if you are sure to use this database and if required upgrade it.

Now all prerequisities are done and you can isntall upgrade.

 
Progress…..

 
.. and finished. Your Veeam Backup & Replication was upgraded to version 9.5
You can connect ..

 
after login as a last step server componnents will be upgraded.

Once done you can use Veeam Backup & Replication and do backups.
Note:
All services which were stopped and disabled before installation are automatically set as Automatic startup.