The truth is that we are really just waving our hands in the air. Just talking about Watts is meaningless. The wattage rating of a loudspeaker usually means the number of electrical Watts you can feed to it from an amplifier, continuously (or not, sometimes!), without causing damage or again, it might mean how much power you can feed it before it starts to distort the sound more than a certain level. Or it might just be a number the maker dreamed up to look good. Computer speakers of the type we are talking about each have an amplifier inside, feeding a drive unit. We can suppose a 10 Watt per channel pair of speakers has an amplifier in each that will happily feed 10 Watts to each drive unit, and that the drive unit will happily take that power indefinitely without overheating or distorting the sound. We can suppose this with a varying level of confidence depending on the quality of design and manufacture. Cheap little no-name speakers will probably perform less well than expensive big ones from a good manufacturer.
Another factor is drive unit efficiency. That is, the ratio of electrical power in, to sound energy out. Some hi-fi speakers use designs to achieve high quality that are very inefficient. You could feed an inefficient speaker with music at (say) 20 Watts and it would just be comfortable listening in an average sized living room. Another, more efficient design would blow your ears off.
Most computer speakers of the type we are discussing are capable of going loud enough to be annoying, even the 5 Watt ones.
These are my speakers, cheap Labtec Spin 95s, and I have just found out they claim to deliver 2 Watts RMS per channel. I can tell you they are perfectly capable of annoying everyone in the house. I have one on each side of my monitor, and I generally have the volume way down. I can use them when I am watching videos or listening to music and they are pretty OK really.
If I was into gaming I might get a set with a third speaker for bass (a subwoofer). If I was really serious I would not bother with computer type speakers at all. I would get a small (say 20 Watt per channel) stereo amplifier or music center and a pair of good but budget-level smallish stereo speakers. Some people repurpose old mini hifi systems.