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

• Table: Common Armor, Weapon, and Shield Hardness and Hit Points - Increase all HP values by 5. Ignore the bit about changing hp values based on size.
• Table: Substance Hardness and Hit Points - Keep as is
• Table: Size and Armor Class of Objects - Ignore completely it's not relevant to 5e
• Table: Object Hardness and Hit Points - Change the Break DCs to as follows: Rope (1 inch diam.) 20 Simple wooden door 15 Small chest 20 Good wooden door 20 Treasure chest 25 Strong wooden door 25 Masonry wall (1 ft. thick) 30 Hewn stone (3 ft. thick) 35 Chain 20 Manacles 20 Masterwork manacles 25 Iron door (2 in. thick) 30
• Table: DCs to Break or Burst Items - Change the Breaks DCs to as follows: Strength Check to: DC If both apply, use the larger number. Break down simple door 10 Break down good door 15 Break down strong door 20 Burst rope bonds 15 Bend iron bars 25 Break down barred door 25 Burst chain bonds 25 Break down iron door 30 Hold portal +5 Arcane lock +10

Smashing an Object
Smashing a weapon or shield with a slashing or bludgeoning weapon is can not be done while that weapon or shield is being wielded by an opponent. Smashing an object which is not being held is an Attack VS the object's AC. Generally, you can smash an object only with a bludgeoning or slashing weapon.

Armor Class
Objects are easier to hit than creatures because they usually don’t move, but many are tough enough to shrug off some damage from each blow. An object’s Armor Class is equal to 10 + its Dexterity modifier. An inanimate object has not only a Dexterity of 0 (-5 penalty to AC), but also an additional -2 penalty to its AC giving it an AC of 3. Furthermore, if you take an action to line up a shot, you get an automatic hit with a melee weapon and advantage to attack rolls with a ranged weapon.

Hardness
Each object has hardness—a number that represents how well it resists damage. Whenever an object takes damage, subtract its hardness from the damage. Only damage in excess of its hardness is deducted from the object’s hit points (see Table: Common Armor, Weapon, and Shield Hardness and Hit Points; Table: Substance Hardness and Hit Points; and Table: Object Hardness and Hit Points). If the object which is being targeted has a hardness which is greater than the item which is being used to smash the object, then the targeted object has resistance (damage is halved) to the relevant damage type.

Hit Points
An object’s hit point total depends on what it is made of and how big it is (see Table: Common Armor, Weapon, and Shield Hardness and Hit Points; Table: Substance Hardness and Hit Points; and Table: Object Hardness and Hit Points). When an object’s hit points reach 0, it’s ruined.

Very large objects have separate hit point totals for different sections.

Energy Attacks
Acid and Thunder attacks deal damage to most objects just as they do to creatures; roll damage and apply it normally after a successful hit. Most objects are resistant to Electricity and fire attacks; divide the damage dealt by 2 before applying the hardness. Cold attacks deal one-quarter damage to most objects; divide the damage dealt by 4 before applying the hardness.

Ranged Weapon Damage
Objects have resistance against ranged weapons (unless the weapon is a siege engine or something similar). Divide the damage dealt by 2 before applying the object’s hardness.

Ineffective Weapons
Certain weapons just can’t effectively deal damage to certain objects.

Immunities
Objects are to critical hits. Even animated objects, which are otherwise considered creatures, have these immunities because they are constructs.

Magic Armor, Shields, and Weapons
Each +1 of enhancement bonus, or each degree of rarity above common, adds 2 to the hardness of armor, a weapon, or a shield and +10 to the item’s hit points.

Vulnerability to Certain Attacks
Certain attacks are especially successful against some objects. Treat the object as if it has vulnerability for the relevant damage type. In such cases, attacks deal double their normal damage and may ignore the object’s hardness.

Damaged Objects
A damaged object remains fully functional until the item’s hit points are reduced to 0, at which point it is destroyed.

Damaged (but not destroyed) objects can be repaired with the appropriate tool.

Saving Throws
Nonmagical, unattended items never make saving throws. They are considered to have failed their saving throws, so they always are affected by spells. An item attended by a character (being grasped, touched, or worn) can not be targeted by spells unless the spell specifies otherwise, in which case they make saving throws as the character (that is, using the character’s saving throw bonus).

Magic items always get saving throws. A magic item’s save modifier are equal to 5. An attended magic item either makes saving throws as its owner or uses its own saving throw bonus, whichever is better.

Animated Objects
Animated objects count as creatures for purposes of determining their Armor Class (do not treat them as inanimate objects).

Breaking Items
When a character tries to break something with sudden force rather than by dealing damage, use a Strength(Athletics) check (rather than an attack roll and damage roll) to see whether he or she succeeds. The DC depends more on the construction of the item than on the material.

If an item has lost half or more of its hit points, the DC to break it drops by 5.

A crowbar or portable ram improves a character’s chance of breaking open a door by adding the user's proficiency bonus, even if they are not specifically proficient.

Final caveat, these rules should be seen as a rules variant, and so replace other rules of the same nature.