how do i totally wipe my 2005 apple macbook

How did the instructions at the site you came from fail: https://support.apple.com/en-us/HT208496

What were the error messages if any?

A "MacBook Air" is not a "MacBook". Many use the term "MacBook" generically to include MacBook, MacBook Air and MacBook Pro.

The MacBook (with no trailing model identifier) is a separate entity all to itself ... technically.

Additionally, how did my question solve anything? I see this from time to time and it doesn't fit; questions don't provide solutions, only request clarifications and/or more information.

There are no 2005 MacBooks, the first MacBook was introduced in 2006.