What you are trying to determine, and not based on the taxpayer's description but based on reality, is:

Trad IRA as deductible or post tax.

Roth eligible or not.

Transfer vs rollover vs in his hands.

Recharacterize is not the same as Conversion.

The $5k might or might not be taxable, and the $500 might be an excess corrections or not, and there might have been earnings or not.