$5.$ In May $2025,$ Brayden converts $$100,000$ in his traditional IRA to a Roth IRA. The value of the assets in the Roth IRA drops by $40$ percent due to a significant decline in the stock market that occurs in October $2025.$ The Roth conversion results in Brayden incurring $$100,000$ of taxable income, when he could have waited and converted only $$60,000($after the $40$ percent drop$).$ Which of the following statements is correct?$$

a$.$ Brayden cannot recharacterize the conversion.$$

b$.$ Brayden can recharacterize as long as it is done within six months from the date of the conversion.$$

c$.$ Brayden can recharacterize after December $31,2025.$

d$.$ Brayden can recharacterize at any time before the due date of his tax return, including extensions.$$