If you're talking about trusting our senses to give us absolutely accurate information about the various things sensed, no, we can't trust them. If you're talking at a practical level, they ordinarily seem quite competent when it comes to informing us about our surroundings. At least by our own standards.
For instance, color doesn't exist. At least as we experience it. Our brains take sensory information and make up shit. And we think we're seeing. And we are, to a certain extent, but not as well as we think. Yet it works most of the time. And as long as it works long enough for us to procreate and raise our young, then that's about all the better our senses really need to work. Everything else is a bonus.
And it doesn't even do much good to walk around aware that our senses are incomplete. We can see only a small portion of the electromagnetic spectrum, and would have much more information about the world if our senses could be broadened to include things like infrared. (Which of course we can do, artificially.) We hear a limited portion of the sounds in our environment. Our sense of smell is putrid (I'm proud of that one). Our sense of touch varies but is probably pretty accurate, overall, and our sense of taste is nice but probably reinterpreted by the brain in much the same way as light is. On top of that, our brain has to process the incoming data in such a way that it makes sense to us consciously. So those things we do sense are not always presented to us in things like chronological order, because our head can't handle it. If you clap your hands, you see it first, hear it second, feel it third, yet your brain tells you all three happened simultaneously. Which is cute, but not accurate enough to applaud.
So no, we shouldn't trust our senses. However, we have little choice. So we do. With caveats that not everyone is aware of.
Of course, when discussions like this start, we should also ask: Do we trust our philosophers? And why?