Q: I have removed 3 of the 5 devices and it still tells me I cant athorize my new laptop Grrrrrr

The easiest way out would be to reauthorize all computers at once, then authorize again only the Onnes you are currently using. See this help page:

Authorize your computer in iTunes - Apple Support

If you run out of authorizations

If one of your 5 authorizations is on a computer you don't use much anymore, deauthorize it. If you've sold or given away a computer that used one of your 5 authorizations, you'll need to deauthorize all of your computers and then re-authorize each one that you still use.

See:  Deauthorize your computer using iTunes - Apple Support

Deauthorize all computers

If you need to deauthorize your computer but you can't access it, you need to deauthorize all computers. This option is available after you authorize 2 computers using your Apple ID. You can deauthorize all computers once per year.

You should deauthorize all computers if:

• Your computer doesn't work anymore.
• You sold or gave away a computer and didn't deauthorize it first.

To deauthorize all computers:Click to open iTunes and sign in to your Account Information page, or use these steps:

1. Open iTunes.
2. If you’re not signed in, sign in with your Apple ID.
3. From the menu bar at the top of your computer screen or at the top of the iTunes window, choose Account > View My Account.
   
   If you’re using Windows and can’t see the menu bar, learn how to turn it on.
4. Enter your password, then press the Return or Enter key on your keyboard, or click View Account.

On the Account Information page:

Scroll to the Apple ID Summary section. To the right of Computer Authorizations, click Deauthorize All.

Room has nothing to do with Authorizing devices. When you indicate you removed 3 of the 5 Authorized Computers, how did you do that?

GB