Upgrade from 4.60.2 to 4.60.5 without losing the design and data

It's simple to upgrade. You can follow this article or follow the below steps:
1. Download latest no-source version or source code depending upon your need. Unzip it as well.
2. Stop your website for a while.
3. Take database and website backup.
4. Replace the unzipped no source or published copy from the source code version without replacing two folders, App_Data and wwwroot with your website folder.
5. Restart the website.

BTW, if the login doesn't work after registering on the website, then it must be an issue related to account activation. May be! Please check.

Best regards,
Atul

The directories  App_Data contains the .json config files
and wwwroot contains any static data
So you do not want to directly overwrite those directories
He is saying everything else can be deleted and replaced with the new version

Although I do not do it that way as if you want to role back you need to stuff around with backups

I prefer to create a new fresh directory and copied in the complete no-source version
Then I run an install to create a new test database and check everything works
Then I copy in any files required from wwwroot and any plugins from the old version directory
Then point the new website appSettings.json file to the old database and run the migration
But that's just the way I do it

Edited: the system will run the migration to upgrade the database as required

Can you explain normally? I use only No Source version.

I don't understand step # 4. Please, explain it.

Can you explain normally? I use only No Source version.

I don't understand step # 4. Please, explain it.
Okay. Let me explain this again. Please follow the below steps:

1. Download the latest no source version. Unzip it somewhere on the server.
2. Place the unzipped directory within the same directory as your current website directory. It should be mostly within C:\inetpub\wwwroot\. Once you have copied, you can rename it to whatever you want.
3. Stop the website from your windows IIS manager.
4. Take a backup of your database.
5. Go to your current website directory, copy and replace App_Data and wwwroot folder from your existing website directory to the new nopCommerce directory from step 2.
6. Go to IIS manager, select your site from the list of sites. Then right click the selected site, go to, Manage Website > Advanced Settings.
7. In the advanced settings dialog box, point the physical path to the new website directory from step 2 and step 5. Click Ok button once done.
8. Once you have completed steps 1 to 7, now you need to provide permissions to the new directory which you just mapped with the site in the IIS. In order to do that, right click on the site and click Edit Permissions menu option.
9. In the edit permissions dialog box, go to the Security tab then click on Edit button.
10. In the edit window, select IIS_IUSRS from the Group or usernames list and make sure that this user has proper permissions. I generally set to full control on the directory.
11. Once done, start the website and try to browse in a private window first. This is the step where automatic migration happens from 4.60.2 to 4.60.5 in this version of nopCommerce.

I can guarantee that this process has no chances for any error if you follow wisely. We upgraded a lot of websites the same way.

Best regards,
Atul