Is there empirical evidence for dark matter and dark energy?

Yes. The question of whether they exist is different from the question of whether there is evidence.For dark matter: Scientists observe rotational motion in galaxies. From the rotation, and our science of gravitation, they can compute how much mass there must be in galaxy to account for that rotation. It turns out that there needs to be a lot more mass than is observed. So the unobserved mass, detected by the gravitational evidence, is called "dark matter."There is, of course, a possibility that there is something wrong with our understanding of gravitation. In that case, perhaps there isn't any dark matter, but instead there is another mystery. So the existence of dark matter isn't at the point where it can be considered a certainty, but it is thus far the best explanation of the evidence. And, of course, it is a research area to find out more about what is happening.For dark energy, the issue is the observations related to the expansion of the cosmos. "Dark energy" refers to the energy that would be required to cause that expansion. Again, there is a possibility that there is a problem elsewhere in our understanding, so it isn't a certainty that dark energy exists. And, again, it is a research area to identify the dark energy or to identify what else is going on.It is a certainty that there is evidence. It is not quite so certain what the evidence means, so further research is going on.

Right. And I have explained what the evidence is. So, clearly there is evidence. "Dark matter" is the name of a scientific mystery (of something unexplained). Similarly, "dark energy" is the name of another scientific mystery.Clearly those mysteries exist.If you are asking whether "dark matter" refers to a huge herd of black cats wandering around inside galaxies, then probably not but the fact is that we not currently have a complete explanation for the evidence that we see. That's why it is considered a mystery. Well, I have been keeping to the facts. And the current situation is that we have evidence (that is, facts), but we do not currently have a complete explanation for that evidence (i.e. we are looking for more facts).When we will have those additional facts, I cannot say. If it takes building a space ship to travel to a distant galaxy, then perhaps we will never have them. On the other hand, perhaps some new astronomical discovery will lead to an "Aha! Insight" moment.