"Playing a Test match here is always special but this week will live in my memory", said Anderson, 35, who made his debut at Lord's in 2003. "There were two hard weeks, but what is most pleasing is the resilience and character to come back from both of those with two extra strong performances", said Root.
"He's a massive part of our dressing room and I'm sure he will be for a long time to come".
A nine-wicket win inside three days at the "home of cricket" meant England had won both of Root's first two series as captain following a preceding 3-1 home triumph over South Africa.
But having been kept waiting for the landmark achievement since going wicketless in the second innings of West Indies' series-levelling win at Headingley, Anderson said his main emotion at breaking the 500 barrier was one of relief. Leg-spinner Devendra Bishoo struck first ball to have Alastair Cook (17) lbw but that merely denied England a 10- wicket victory.
This was England's last Test before they begin the defence of the Ashes in Brisbane in November.
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"In the second innings Jimmy was outstanding".
He crushed West Indies with his 243 at Edgbaston.
Stokes (60) notched his 12th Test fifty as the hosts scored 194 to earn a 71-run lead on first innings - Stuart Broad also contributing with a dashing late 38 that featured four fours and two sixes. However, Australian skipper Steve Smith continues to be on top.
"But Shai Hope batted extremely well and we have a lot of positives to take", added the all-rounder.