"I don't know however if the distribution was after the rollover was completed or during the process of the rolling over of investments."

Yes, you do; Look at the issuer names on the 1099-R to see what happened because of who reported it. Was the 1099-R for the distribution out of that "new Roth IRA" or out of that ex-employer's Designated Roth? Or, was the Designated Roth paid out to your taxpayer, who only rolled over some of it to the new Roth account?

"What further information do I need"

All of this matters.

"or do I consider the amounts in box 5 of the 1099-R rollovers"

Wait; now you used Plural for Rollovers? Plural?

"as the basis of the distribution on the 1099-R with the code J in box 7?"

"Basis" is the amount the taxpayer contributed. It is not Earnings. Yet, the amount a leaving employee would be entitled to take or roll would be the entire account balance, including any earnings from the past 11 years.