Currently most of the pictures that I want to put into a my portfolio are around 3000 x 5000 px. It is obvious that most people don't have a screen resolution even close to this. Is there a standard size for online photos?
The optimal size depends on a lot of things. The intended audience, the quality of your work, the license you use and the watermark if applicable.
Most of my professional friends limit themselves to about 600x600 to avoid illegal copying. This obvisously limits the ability to appreciate photographic details but this is the one I chose too because people steal online images constantly.
Unfortunately photo buyers sometimes as for full-size (or close to) previews in which case you can use a service with private access to show these.
If you want to give an immersive experience you will need a higher resolution. A minimum of 900px on the wide side but up to 1400px would not me unreasonable. In that case you will probably want to place an intrusive watermark over the center/subject of the image or content yourself if an open licence which, sadly, will probably not be respected anyway.
Online images get copied and even printed, so limiting to a small size which cannot be used printed is key to keep your property from being abused.
Currently, the majority of people browsing the web are using monitors with a resolution around 1366x768.
I'm at 1920x1200.
So what I've done is set the largest side to 950 pixels, and let the smallest one fall where it will.