Adam Clarke on Acts 24:1

After five days - These days are to be reckoned from the time in which Paul was apprehended at Jerusalem, and twelve days after he had arrived in that city; see Act 24:11. Calmet reckons the days thus: - St. Luke says that Paul was apprehended at Jerusalem when the seven days of his vow were nearly ended, Act 21:27; that is, at the end of the fifth day after his arrival. The next day, which was the sixth, he was presented before the Sanhedrin. The night following, he was taken to Antipatris. The next day, the seventh, he arrived at Caesarea. Five days afterwards, that is, the twelfth day after his arrival at Jerusalem, the high priest and the elders, with Tertullus, came down to accuse him before Felix. - But see the note on Act 23:32.

A certain orator named Tertullus - This was probably a Roman proselyte to Judaism; yet he speaks every where as a Jew. Roman orators, advocates; etc., were found in different provinces of the Roman empire; and they, in general, spoke both the Greek and Latin languages; and, being well acquainted with the Roman laws and customs, were no doubt very useful. Luitprandus supposed that this Tertullus was the same with him who was colleague with Pliny the younger, in the consulate, in the year of Rome, 852; who is mentioned by Pliny, Epist. v. 15. Of this there is no satisfactory proof.