Kumar finished with the second-best figures for an Indian bowler at Lord's after Amar Singh's six for 35 way back in 1936.
This was also his second five-wicket haul of the series and has come in successive Tests. He had taken five for 82 at Trent Bridge last week.
Ravindra Jadeja (2/46), Moahmmad Shami (1/58) and Murali Vijay (1/12) were the other wicket-takers for India in this innings. Ishant Sharma (0/61) and Stuart Binny (0/45) weren't rewarded for their efforts despite bowling well on day two.
With the second new ball only six overs old from the previous evening, the Indian bowlers would have been licking their lips.
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However, Shami and Ishant were poor in their initial spells, losing all discipline from yesterday and bowling wayward lines. It allowed Matt Prior (23 runs, 42b 4X4) and Liam Plunkett (55 not out, 79b, 8X4) to score quickly.
Hitting eight boundaries, the duo brought up their 50-run partnership off only 74 balls in the 95th over.
It sparked off a mini-collapse with Kumar, who came into the attack, dismissing Ben Stokes (0) and Stuart Broad (4) in the 99th over. England had lost three wickets for 15 runs in the space of 26 balls.