Before I say anything else, I'll say this: If one wants to use "Strength Bows" in 5E...whether the way they were done in 2E, 3E, or other...then do so. It's your game. It probably won't "break" it. And if it's something you and your group like, then it will be fun for you and your group...and that's really all that matters. Just understand that there are problems that can arise, as Majoru Oakheart highlighted (more on this in a bit).
However, there are a lot of misconceptions about bows; and many of them have popped up here in this thread.
Firstly, neither the 2E or 3E mechanics for "Strength Bows" are realistic. These mechanics do not describe how real bows work. All they do is satisfy the "rule of cool" for some players and groups; which is really all the reason one needs for using them. Just don't live under the illusion that this is more realistic.
Now, more on what Majoru Oakheart said:
The real problem is that if you can use the best ranged weapon in the game(Long Bow) using strength then you can create a character who only needs one stat to simultaneously be the best at melee weapons, AC, and ranged weapons..
It requires no tradeoffs at all to be the best at literally everything..
And this is the crux of it. Majoru is absolutely right.
Not to mention, as I said above, that the 2E and 3E mechanics for this are not realistic.
English Longbow Archers...the ones of the late medieval...the ones that used bows with pulls of anywhere from 150 lbs. to 200 lbs., did not have high strength.
What they did have was high "specialized" strength.
These men most likely had average overall strength; basically, strength scores of 10 to 12. They were able to pull these incredibly high draw-weight bows because they participated in specialized training from the time they were kids; building up to stronger and stronger bows.
Being able to pull a 200 lb. bow does not mean they could also lift 200 pounds single-handed. Lifting a weight requires a much larger part of all of your body's muscles. Pulling a bow is a "specialized" muscle movement; one that uses a very specific set of muscles.
So, what would be "accurate" or "realistic" then, if strength-bow mechanics aren't?
One, such weapons are Specialized Weapons. They are not part of a larger group; not even martial weapons.
Two, those who use such weapons are specialized to use them.
That means either using Feats (if Feats are used in your game), or using specific class-builds (archetypes), and NOT basing this off of a Strength score.
So, either allow such bows only for Archer archetypes, or make a Feat to give proficiency in these weapons. Also, model their increased damage in the damage die/dice of the weapon, not in a strength bonus.
Next:
You could merely create a new Weapon Property specific to the longbow whcih is the antithesis of Finesse...
There is no justifiable reason, whether for cool factor or realism, to restrict something like this to only longbows. Composite short bows can be just as powerful, and can be just as hard to pull.
...(limit it to longbows to start), and if it doesn't throw things out of whack, maybe branch out to heavy crossbows (stronger gears,pulleys,etc).
"Gears and pulleys" do not make bows more powerful. Crossbows are more powerful because they can use stronger materials (whether stronger, thicker wood, or steel, or composites...including modern composites), and uses mechanical leverage to "draw" the bow (something a human simply isn't strong enough to do without that mechanical leverage).
Compound bows, which use pulleys, do so to make it easier to hold a draw. The pulleys on a compound bow do not make it more powerful. In fact, some potential energy is actually lost due to the pulleys (friction, effectively longer bowstring than a comparable sized bow causing more power lost to elasticity, etc.).
Simply change ranged weapons to use Dex to hit and Str for damage.
Thats more realistic anyway.
No. This is not more realistic.
Using Dexterity to hit means focusing on speed and accuracy to bypass defenses. More speed means more energy imparted to the target, and thus more damage. Better accuracy means hitting more vulnerable locations, and thus more effective damage. Using Strength to hit means focusing on brute force to overcome armor and defenses; to blast through it...and also means more damage.
It's like asking, "Which causes more damage: a stiletto to the heart, or lopping off a limb?"
Or if that's too apples and oranges, how about "Which causes more damage: A perfectly placed arrow shot to the chest with an armor piercing arrow, or a lance strike to the chest wielded by a mounted knight at full charge?"
Answer: BOTH! BOTH Strength and Dexterity add to damage.
What about having a feat take care of this?
LONGBOWMAN
Thanks to extensive practice with longbows, you gain the following benefits:
• You may add your STR bonus, instead to your DEX bonus, to damage rolls when attacking with a longbow that you are proficient with.
• Being within 5 feet of a hostile creature doesn’t impose disadvantage on your ranged attack rolls.
• When you make a ranged attack with a longbow that you are proficient with the range increases to 200/800.
• Before you make a ranged attack with a longbow that you are proficient with, you can choose to take a - 5 penalty to the attack roll. If the attack hits, you add +10 to the attack’s damage.
Again, why only Longbows? Even in the real world, composite short-bows have much the same damage and range potential. Why purposely gimp certain player choices over others, especially when doing so makes neither game-play sense or reality sense...and even violates the rule of cool?
There's no upside to this...except for those that like longbows...
Compound bows have pullies to make the draw easier, and as such there is no str requirement.
Wrong. Compound bows have pulleys to make it easier to HOLD a draw. Initially, the "pull" is the same as any other bow until about two-thirds of the way through the draw. Then, the "pull" drops off about 30% to 40%; making it easier to hold the draw. In other words, a 100 lb. pull compound bow still requires 100 lbs. of force to pull for the first two-thirds of the draw, and then about 60-70 lbs. to hold the draw.
Along with what I said earlier about this not making compound bows more powerful, it does have the effect of making it more accurate for non-specialist archers...because they can hold the draw longer, with less effort, making it easier to aim and release when the shot is best. For someone trained in pulling a high-strength bow, that can already easily pull and hold a large pull, the effect would negligibly add to accuracy.
