Belichick will take the top 5 pick and trade down anyway
So I did some boolean on this and asked "top 10" as far as traded out of vs just Top 5. My memory said he didn't trade "out" when he had a low pick - he might trade "down" if he thought he'd still get his guy. Given there isn't really any data from top 5 since he won too much to get there there often I did find the following:
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No team deals on draft night quite like the New England Patriots. Since taking over the Patriots in 2000, Bill Belichick has executed a total of 77 trades during the NFL draft. With the 2020 edition set to kick off Thursday night, we took a look back at Belichick’s 10 best (and five worst)...
nesn.com
4.
2003: Acquired Baltimore’s second-round pick (No. 41 overall, TE Bennie Joppru, by Houston) and a 2004 first-round pick (No. 21 overall, DT Vince Wilfork) in exchange for a first-round pick (No. 19 overall, QB Kyle Boller)
By allowing the Ravens to climb the board for Boller, the Patriots were able to land one of the top defensive tackles in franchise history the following year. They also included the 41st overall pick in a subsequent trade that landed them productive safety Eugene Wilson (36th overall, 2003).
5.
2007: Acquired San Francisco’s 2008 first-round pick (No. 7 overall, DT Sedrick Ellis, by New Orleans) and a fourth-round pick (No. 110 overall, CB John Bowie, by Oakland) in exchange for a first-round pick (No. 28 overall, OT Joe Staley)
Looks one-sided on paper, huh, with the Niners landing a franchise left tackle in Staley? Not so. The Patriots used that future first-rounder to trade down and select linebacker Jerod Mayo at No. 10 overall in 2008 (and add a third-round pick they used on bust Shawn Crable). The fourth they received gave them the ammunition to swing the Moss trade.
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However, if your wider point is simply trading on draft day regardless of position - that seems 100% true. 2002, 03, 06, 07, 09, 10, 17, 18 (just what I could find quickly - it's probably every year frankly) all had one or more moves regardless of draft position. Very active.