Just an observation, SF writers Eric Flint/Dave Weber wrote about a naval battle between ships from the 1600’s and ships built on a Civil-War level of technology (it’s a SF thing, time-travel and all that). It did not end well for the older vessels. (Book is 1634: The Baltic War if anyone is interested).
I would also note that folks are promoting the ships to 18th/19th levels of technology, while the OP is talking about 1625 or so. Ships were much small and much less heavily armed at that time (HMS Victory could have whipped almost any 1620’s Navy all by itself) along with generally smaller guns and longer load times. So even in the best instance (surprise at docks), the 1600’s ship is only going to be firing a broadside of 30 or 35 guns, and half of them will be lighter (12 and 18-pounders) weapons for clearing an enemy’s decks or damaging his sails.
So yeah, they could inflict some damage, but not a lot and they would be dead meat soon enough.
As for HMS Victory, I’ve actually seen her in person (visit Portsmouth Harbor, England if you get a chance) and the one thing you notice is how small she is, compared to even ‘light’ warships today. Per Wikipedia, HMS Victory is 228 feet long, 52 feet abeam, and has a draft of 29 feet. An Arleigh Burke is 505 feet long, 66 feet abeam, and has a draft of 31 feet.
And it has a rated broadside (again per Wikipedia) of 15 32-pounders, 14 24-pounders, 22 12-pounders and a 68-pound carronade. That equals about 1,150 pounds of shot per broadside, and those 12-pound balls are unlikely to get through even the thin armor of a modern-day ship (IMHO…I’m willing to be proved wrong).
So yes, in a absolute surprise at a range of less than 50 yards, the Victory (provided it’s guns were already loaded), could probably inflict some damage and with a battle-tested crew could probably get off a broadside every 90 seconds or so (number came from this site: http://www.hms-victory.com/things-to-see/original-gun), but except for the carronade getting a Golden BB shot, I don’t see how it could do enough damage before the 5" gun was manned and blew a hole in her bottom.
IMHO as always. YMMV.