Article from FOX SPORTS mention:
These three successful reviews happened in the space of six deliveries, from the same bowler to the same batsman.
It’s been reported no player has successfully appealed as many “out” decisions in a Test innings previously, let alone in the space of an over.
Ali would survive a further two DRS appeals throughout his innings, both reviewed by Bangladesh after the batsman had been given not out.
So it is clear that 5 reviews against Moeen Ali is the highest against a player in an innings during a test match until now. So no player has survived more player reviews.
And from same article:
when Stuart Broad successfully appealed the umpire’s decision against him at the start of day two, it set a new record (nine) for most reviews used in a Test innings.