Well I'd hate to get complicated for $5.50, I believe the technically correct way to record this would be:
step 1: purchasing the logo: credit cash (or however you paid), debit intangible assets
step 2: you decided that the logo is worthless: credit intangible assets, debit write-offs (an expense account).
Depending on how complex your accounting system is, you may just have one write-off account or you may have many.
As long as you retain legal rights to the logo, it is debatable if you can write it down to zero. As long as you retain the right to use it in the future, this implies that you believe it has some potential value. Though I can't imagine an auditor is going to pursue this very far for something that cost $5.50. If you had invested $10,000 in developing the logo, that would be a different story.