Book request: biology of sensation and perception
This is a very broad range of topics. I doubt you'll be able to find a single reference on all of it. I'm providing below some references with a focus on more introductory approaches.


  The mechanisms underlying our “five senses,” i.e. the eye, inner ear, tongue, nose, and nervous system, and how (chemically/physically) they are triggered


Bear, Connors &amp; Paradiso "Neuroscience: Exploring the Brain" is pretty extensive. It covers chemical senses, vision, audition, the vestibular system and touch. It is not cheap, but that's the only reference that will cover most of the topics you are interested in. However it focuses mostly on the physiology of the senses, and not really about perception

Otherwise I'm afraid you'll immediately have to read specialized books such as Palmer's "Vision Science", Moore's "introduction to the psychology of hearing", Goldberg et al. "The vestibular system". Those are fairly readable introductory books. I don't know much about chemical senses.


  How our brain makes inferences from the raw sensory data we receive, e.g. using our depth perception to infer distance from a two-dimensional projection onto each of our eyes


For the topic of inference specifically a classical reference is Richard Gregory's "Eye and Brain: The Psychology of Seeing". It is dated (60s) but still very relevant. This is somewhat contradictory with your first point because inference is a behavior while you asked for more physiological references. Stereopsis specifically is a classical field of vision science so any descent book will cover it.


  Comparison with other species of animals


I cannot recommend enough Sarah Shettleworth's "Cognition, evolution, and behavior". Though focusing only on behavior, it is a very extensive and interesting book.


  Experimental results relating to the three points above


Any good book would include data and plots from classical experiments.


  An evolutionary perspective hypothesizing about why these sense-detecting organs were important for human survival


Again, Shettelworth's book.