You have to try it and see, but also don't forget there's a difference between "destroyed" and "combat ineffective".
The problem is that CT:HG does not reflect this. Unless you receive a Ship
Vaporized critical, even if a ship is reduced to 0 in all its factors (excoept those that can not be reduced, as size or config, off course) it can be taked by the "battlefield" holder at the end of the battle for repairs, that won't take too long.
Both a 5K and 30K ships can be geared up to max armor, agility, computer and maximum number of turrets.
Statistically, the 5K ships cost more per ton than a 30K ship, that means for the same price, you can only show up with 5 5K ships for the price of a 30K ship, and leave money on the table. That gives the 30K ship a pretty solid advantage and it can simply bring more guns to the fight.
If you field 6 5K ships vs the 30K ship, then it's basically a wash. The 30K ship offers no real advantage, and the 5K ships aren't small enough to offer an advantage to them. The only real advantage of the 5K ships is they bring a lot more Fuel hits, so can soak up some more free hits, in the large, than the 30K ship. But I don't think the combat would last that long that it would come in to play.
OTOH the cruiser spinal would mean one hit/one kill. A J rated meson gun will hit on a 10+ (4+, -6 due to agility), and any hit will cripple a ship. And the 5 kdt ships are unlikely to have powerful meson screens...
Bring in 25-30 1K DDs vs the 30K ship, and it may very well be a different story. The 1K ships are small enough to get the -1 targeting DM, but large enough that they can't be critted by anything but a Spinal. That may be enough to turn the tide, even with a few less ships. 30 1K vs 1 30K is definitely in the 1K's favor.
(also to all similar posts)
From the Budget POV, each of those small ships will need a máximum rated computer to be efective, and, at TL 15 (that's where I doubt about the escorts usefulness) that means Mcr 140 per ship only for its computer...
And again, this can work in single engagement contests, under the rules for TCS, but not so sure in a campaign, that (IMHO) represents more the fleets needs.
In such a campaign, the ships are likely to be more dispersed, and the time dispersal on arriving to a destination should be a factor, if the destination point is defended (A GG, a Main planet, etc), though that would mean some minimal operational rules...
Another factor to take into account, and I've told about it some times, is the rule about crew quality (CT:HG page 44).
If each side can have (let's say) an OC with ship tactics 3 and a pilot with skill 3 (that I don't believe to be so rare), the cruiser will have both, with its +1 to computer and agility ratings, while only one hamster will have it, And this simple fact may well be decisive.
As I already suggested time ago for TCS contests, just where it says 100 pilots per side add 1 of them skill level 5, 3 of them skill level 3, One OC ship tactics skill 5 and 3 at 3 (I don't find those levels too high among 100 pilots), and see how it changes on a single ship (or a few of them) against swarms of hamsters.
And in a campaign the effect of those key individuals should be used...