I have looked in the player handbook and it does not seem very clear on character vision. In Bright light how far can characters see? For example if I have a player with the feat sharpshooter and have a long bow I can shoot 600'. Is there anywhere that talks about how far you can see in bright light? Dim light? Also for example if a character can read lips it doesn't specify distance away in which this is possible.
[RPG] How far can you see? (targets, lip reading etc)
dnd-5evision-and-light
Related Solutions
There are distance limitations on Perception checks in the rules, establishing that sight is not limited only by cover or lack of light. The limitation doesn't appear to be an abstraction of cover since the likelihood of nearby cover is also mentioned apart from the distance limit. Based on the reasoning given in the various terrains, it appears that distance limitation represents an abstract combination of terrain folds, vegetation, distortions in the air, and simply the inability for an observer to distinguish an object from the background on which it visually sits. (See the part about visibility in mountains being both a very short number and alternatively very far as determined by the DM's map of ridgelines, and the visibility in the desert being limited in part by heat shimmers in the air.) Furthermore, these limitations are mentioned in addition to limitations caused by obstructions to light of sight, making these limitations explicitly apply even when you have line of sight and the target is not in cover:
In plains terrain, the maximum distance at which a Perception check for detecting the nearby presence of others can succeed is 6d6 × 40 feet, although the specifics of your map might restrict line of sight. Cover and concealment are not uncommon, so a good place of refuge is often nearby, if not right at hand.
Unfortunately, in the set of terrains they failed to include an aerial "terrain" or even an above-water terrain, so there are no rules-as-written distance limitations for flying creatures outside of terrain like forest (where the canopy would restrict vision between creatures on foot and in the air). The limitation in plains terrain is 6d6×40 feet, but I don't think anyone could convincingly argue that this applies to flying creatures, given the rules-as-written distance limitations in mountains (as mentioned above).
However, the precedents in RAW strongly imply that there is a limitation based solely on the fact that air can obstruct vision optically, but the DM is on their own to figure out what it should be. There is no RAW answer. Personally I would either try to develop a table based on real-world principles of visibility, or I would build something more game-able like "1 mile per size category" or something to that effect.
You can see light at any range
I did some googling, and while it's pretty hard to find specific citations from scientific studies, the places that I've been able to find say that the human eye can see a candle from somewhere between 10 and 30 miles away. The curve of the Earth is about 3 miles away. Thus, any significant light is at least barely visible from any range that you're likely to have line of effect. The houserule that I've used for a while now is that you can see a light source at ten times the distance that you can see a non-lit object without penalty.
That said, the vision rules in every edition of D&D that I've seen are actually reversed. They only work if both the looker and the looked-at are in the same lighting conditions. The vision rules on PHB 183 state:
In a lightly obscured area... creatures have disadvantage on Wisdom(Perception) checks that rely on sight.
A creature in a heavily obscured area effectively suffers from the blinded condition.
Nothing in those rules says that you can't see a creature if that creature is inside darkness and you aren't. This is clearly ridiculous. This weirdly reversed rule has existed since at least 3.0, and shows how little the designers thought about what to do about differing light conditions.
What this means is that you should rely on your intuition more than the rules for what will give penalties based on vision. Since, IRL, lights can be seen from the horizon, you can probably see someone with a torch from at least a few hundred feet, probably out to a mile or so.
As far as being blinded is concerned, my intuition was always that that penalty happened because you couldn't see the ground beneath your feet, or the things that are around you. Thus, I would rule that a character who can see a light hundreds of feet off is still blinded, except for the purposes of making checks or attacks against targets who are lit up.
Best Answer
The 5e player's handbook does not have rules on visibility, but the DMG does. They can be found on page 243, under the "Visibility Outdoors" heading.
The basic summary of it is that, on a clear day, you can see 2 miles, or until your view is obscured by terrain features. If it's raining, it usually cuts it down to 1 mile. Fog cuts it down to 100 to 300 feet. And standing on a mountain or similarly elevated place will give you a visibility of 40 miles. For comparison, the horizon on earth is 2.9 miles away at ground level.
Dim light isn't mentioned as diminishing your visibility (beyond giving disadvantage on Perception checks), so dim versus bright light doesn't change anything.
As for the range at which you can read lips, there's no specific rules on this. Ask your DM if you can read the lips, or if you need to get closer.