Would there be any major balance concerns with porting the Breaking & Entering rules (specifically the tables contained within, but also possibly adjusting DCs) from 3.5 to 5e?
Only very small issues–hit points and hardness should be okay.
The relative scale of hit points (that is, how many hit points represent a given amount of damage) is essentially static from 3.5 to 5e, so in terms the raw hit points of materials should be unchanged. In addition, the damage output of characters, at low levels at least, is about the same in 3.5 and 5e. Thus, a given character will take about the same time to break through a material using damage in 3.5 and 5e, if you use the 3.5 Breaking and Entering rules.
Assuming that you want the effect that these rules created in 3.5, you can simply take the rules for hardness and item hitpoints wholesale, and put them in your 5e game.
There's actually only one conflict between the two rulesets, and that's the rules for manacles. The manacles in 3.5 had a hardness of 10 and 10 hit points, while the manacles in 5e have 15 hit points, with no hardness, since there's no damage reduction in 5e. The 5e manacles are much easier to break–using a Greataxe with a Strength of 14, in 5e, you have a 95.14% chance to break them in three hits, while in 3.5, you have only a 0.23% chance. This creates a significant gap between the effect of the rules in 5e and 3.5, but nothing will actually be broken if you use the 3.5 rules. If you ever see a published adventure with manacles, just note that the 5e default rules make them much easier to break than the 3.5 rules.
The Break DCs might take some numerical adjusting.
Due to 5e's much-discussed bounded accuracy, DCs from 3.5 should be adjusted significantly downward. For purposes of comparison, in 3.5, a moderately optimized level 20 character could reasonably have a Strength of 30. In 5e, assuming no magic items, attributes are hard-capped at 20.
To determine new DCs, I would look to the "Typical Difficulty Classes" table, on p. 58 of the D&D Basic Rules. This table gives rough example DCs–for example, you might rule that breaking down a good-quality wooden door is "Medium", so you could assign it a DC of 15. Another rough guide might be the relative break DC of manacles, which have a Break DC of 26 in 3.5, and take a DC 20 Strength check to break in 5e.
In general, if my mathematical instincts are correct, to convert 3.5 DCs to 5e DCs, you'll want to only mildly lower DCs that are already low, while more drastically lowering higher DCs.
Initially I thought it would be simple and intuitive to port over the rules from 3.5 to 5e, and it likely still is. However, there are a few rules that I think need to be modified, and for the sake of clarity I have re-written them.
For the tables I recommend the following
Final caveat, these rules should be seen as a rules variant, and so replace other rules of the same nature.