Will experimenting with tunings (specifically tuning my guitar to open D5) have any affect on my guitar or the strings? I've read a few comments that claimed it would. I tried searching on the internet for an answer, but couldn't really find anything.
There area some concerns that could be associated with different tunings for you guitar but in lots of situations those are negligible. As mentioned in the comments, the potential for these concerns would largely have to do with what type of guitar you are playing. The things that come to mind immediately are the concern of breaking strings or that of affecting the guitar's neck and potentially bridge and body.
Tuning your strings up will increase the potential to break them. The increased tension goes beyond that which the strings are rated for, which can cause breakage or decreased longevity. The further up you tune from the intended frequency, the more like you are to break a string.
The more concerning potentials are that of the long term effects to the instrument but they are less likely to happen, depending on the severity of the change. The bridge, neck and body are all intended to hold a certain range of tension and when there is a large enough difference, damage can occur.
If your tension is too high, it can pull your neck in such a way that it will bow to the point that the action (distance between strings and fretboard) will increase. If this goes too far it could be irreversible but that isn't incredibly likely. This is most likely to happen when a guitar is left tuned and unplayed for an extended period of time and can occur even if it is in standard tuning. This should take quite a while to happen but the higher you tune the strings, the faster it will occur.
The bridge could potentially get ripped off. This is less likely on an electric guitar. I had a classical acoustic (nylon string) that someone decided to put steel strings on and the bridge ripped right off. This most likely happened because of the difference in tension that the steel strings required compared to the nylon. So this would be less likely to happen with a steel string acoustic bit still more likely than with an electric, due to an electric have screw that can have a deeper anchor in the body, while an acoustic does not have this option.
Lastly, there could be concern for the body of the guitar but this seems the least likely. You would need to have such drastic difference in tension across the strings that one side is pulling much harder than the other and the disparity of tuning the I imagine would require this would probably not have any functionality. Again, this is considerably more likely to happen on an acoustic than an electric.
In short, you probably don't have anything to worry about (as far as damage goes) when tuning just a step or so up. The things to avoid would really be increasing tension very drastically and leaving it tuned for an extended period of time without playing. Getting strings that are more properly gauged for the tuning you are playing can greatly reduce the change in tension from a standard tuning.
As a side note, the biggest problems that a guitarist will face in using different tunings would be intonation issues and strings not sustaining the notes or sounding floppy/getting fret noise from being too loose. When a guitarist intends to consistently play in alternate tunings, I recommend taking it to a luthier to have it set up properly to maintain intonation across the neck and all strings. Ideally you would have a guitar dedicated to each alternate tuning to have the best intonation from song to song.