So England ultimately won the series against Sri Lanka 2-0, but there were some periods in both Tests where it seemed that the hosts had a chance of winning.
In the second Test, Lasith Embuldeniya took 7 wickets in the first innings and went on to take his first “tenner” in the match. It may have escaped notice that Lahiru Thirimanne took 5 catches as a fielder in the first innings, all of them off Lasith’s bowling.
See the scorecard: https://www.espncricinfo.com/series/england-in-sri-lanka-2020-21-1242951/sri-lanka-vs-england-2nd-test-1243016/full-scorecard
There are several instances of non-keepers taking 5 catches in an innings:

However, Lahiru Thirimanne is the only one who took all 5 catches off the same bowler.
There are a few instances of a fielder taking 4 catches off the same bowler, as that of J Blackwood doing so against Sri Lanka off the bowling of KC Brathwaite. (That was a fluke instance as he never took 4 wickets in an innings in any other Test).
There is at least one instance for India. AL Wadekar took 4 catches off BS Bedi in an innings at Christchurch in 1967-68.
While Lasith took a further 3 wickets in England’s second innings, Thirimanne failed to take another catch. However, his 5 catches off the same bowler may also be a match record in all Tests.