After distinguishing two types of knowledge, knowledge of things and knowledge of truths, Russell devotes this fifth chapter to an elucidation of knowledge of things. He further distinguishes two types of knowledge of things, knowledge by acquaintance and knowledge by description. We have knowledge by acquaintance when we are directly aware of a thing, without any inference. We are immediately conscious and acquainted with a color or hardness of a table before us, our sense-data. Since acquaintance with things is logically independent from any knowledge of truths, we can be acquainted with something immediately without knowing any truth about it. I can know the color of a table "perfectly and completely when I see it" and not know any truth about the color in itself. The other type of knowledge of things is called knowledge by description. When we say we have knowledge of the table itself, a physical object, we refer to a kind of knowledge other than immediate, direct knowledge. "The physical object which causes such-and-such sense-data" is a phrase that describes the table by way of sense-data. We only have a description of the table. Knowledge by description is predicated on something with which we are acquainted, sense-data, and some knowledge of truths, like knowing that "such- and-such sense-data are caused by the physical object." Thus, knowledge by description allows us to infer knowledge about the actual world via the things that can be known to us, things with which we have direct acquaintance (our subjective sense-data).

According to this outline, knowledge by acquaintance forms the bedrock for all of our other knowledge. Sense-data is not the only instance of things with which we can be immediately acquainted. For how would we recall the past, Russell argues, if we could only know what was immediately present to our senses. Beyond sense-data, we also have "acquaintance by memory." Remembering what we were immediately aware of makes it so that we are still immediately aware of that past, perceived thing. We may therefore access many past things with the same requisite immediacy. Beyond sense-data and memories, we possess "acquaintance by introspection." When we are aware of an awareness, like in the case of hunger, "my desiring food" becomes an object of acquaintance. Introspective acquaintance is a kind of acquaintance with our own minds that may be understood as self-consciousness. However, this self-consciousness is really more like a consciousness of a feeling or a particular thought; the awareness rarely includes the explicit use of "I," which would identify the Self as a subject. Russell abandons this strand of knowledge, knowledge of the Self, as a probable but unclear dimension of acquaintance.

Russell summarizes our acquaintance with things as follows: "We have acquaintance in sensation with the data of the outer senses, and in introspection with the data of what may be called the inner sense—thoughts, feelings, desires, etc.; we have acquaintance in memory with things which have been data either of the outer senses or of the inner sense. Further, it is probable, though not certain, that we have acquaintance with Self, as that which is aware of things or has desires towards things." All these objects of acquaintance are particulars, concrete, existing things. Russell cautions that we can also have acquaintance with abstract, general ideas called universals. He addresses universals more fully later in chapter 9.

Russell allocates the rest of the chapter to explaining how the complicated theory of knowledge by description actually works. The most conspicuous things that are known to us by description are physical objects and other people's minds. We approach a case of having knowledge by description when we know "that there is an object answering to a definite description, though we are not acquainted with any such object." Russell offers several illustrations in the service of understanding knowledge by description. He claims that it is important to understand this kind of knowledge because our language uses depends so heavily on it. When we say common words or proper names, we are really relying on the meanings implicit in descriptive knowledge. The thought connoted by the use of a proper name can only really be explicitly expressed through a description or proposition.

Bismarck, or "the first Chancellor of the German Empire," is Russell's most cogent example. Imagine that there is a proposition, or statement, made about Bismarck. If Bismarck is the speaker, admitting that he has a kind of direct acquaintance with his own self, Bismarck might have voiced his name in order to make a self-referential judgment, of which his name is a constituent. In this simplest case, the "proper name has the direct use which it always wishes to have, as simply standing for a certain object, and not for a description of the object." If one of Bismarck's friends who knew him directly was the speaker of the statement, then we would say that the speaker had knowledge by description. The speaker is acquainted with sense-data which he infers corresponds with Bismarck's body. The body or physical object representing the mind is "only known as the body and the mind connected with these sense-data," which is the vital description. Since the sense-data corresponding to Bismarck change from moment to moment and with perspective, the speaker knows which various descriptions are valid.

Still more removed from direct acquaintance, imagine that someone like you or I comes along and makes a statement about Bismarck that is a description based on a "more or less vague mass of historical knowledge." We say that Bismarck was the "first Chancellor of the German Empire." In order to make a valid description applicable to the physical object, Bismarck's body, we must find a relation between some particular with which we have acquaintance and the physical object, the particular with which we wish to have an indirect acquaintance. We must make such a reference in order to secure a meaningful description.