Not top 5 examples, but close:
He'd take the best 3-4 DE of his era (Seymour—6th)
He’d trade down (7th, then traded for 10th—Mayo)
What led up to that Mayo pick makes for an interesting parallel.
In September 2006, BB had traded WR Deion Branch to Seattle for their 2007 first rounder, which turned out to be the #24 overall (WR Cooks -> #23 from the Rams). Going into the 2007 draft, then, BB had the #24 and #28 (the Pats own pick).
In 2007, BB used the #24 on Safety Brandon Meriweather,
and traded the Pats own #28 pick forward - to the Niners for their 2008 1st-rounder and their 2007 4th (which was traded to Oakland for Randy Moss).
Aside from trading their 2nd-rounder (#60) and a 7th to Miami for Wes Welker, the rest of the Pats 2007 draft was pretty much a washout.
[SIDEBAR: BB also traded the Pats 2007 3rd-rounder (#91) forward for Oakland's 2008 3rd + and 2007 7th.]
Anyway, that 2008 1st from the Niners ended up being the #7 over all,
AND the Pats only 1st-rounder after Goodell confiscated the Pats own pick (#31) in the "Spygate" penalty.
BB traded the Niners' 2008 #7 to NOLA for their #10 and their 2008 3rd (#78, used to select Shawn Crable, unfortunately).
[SIDEBAR: He also traded the "forwarded 3rd" from Oakland (#69)
forward again - to San Diego for their 2009
2nd + their 2008 5th (which was used to select Matt Slater).]