There are multiple terminologies for English grammar. Some count the infinitive as a "mood" alongside indicative, imperative, interrogative, and subjunctive, and some don't. (And some include a "conditional" mood.)
The infinitive is different from the other things called moods, because the others all describe "finite" uses of a verb: uses where a verb agrees in person and number with its subject and somehow asserts something about its subject—or asks, or commands, or supposes, these all being different "moods" of predication, i.e. saying something about something. An infinitive does not agree with its subject, as in "Make him leave", and does not even need a subject, as in "It's time to leave."
So, grammarians who want to classify all these ways of using a verb under a single heading have called the infinitive a "mood" and grammarians who want to emphasize the difference between the infinitive and all the finite "moods" have excluded the infinitive. Here is the Oxford English Dictionary's definition of infinitive:
[as a noun] Gram. The infinitive 'mood' or form of a verb.
[as an adjective] Gram. The name of that form of a verb which expresses simply the notion of the verb without predicating it of any subject. Usually classed as a 'mood', though strictly a substantive [i.e. a noun] with certain verbal functions, esp. those of governing an object, and being qualified by an adverb.
The OED's definition of mood explains why it seems reasonable to consider the infinitive a type of mood:
Gram. Any one of the several groups of forms in the conjugation of a verb which serve to indicate the function in which the verb is used, i.e. whether it expresses predication, a command, a wish, or the like; that quality of a verb which depends on the question to which of these groups its form belongs.
So, it is a somewhat arbitrary choice whether you count the infinitive as a mood. This means that there will be raging fanatics who will castigate anyone who makes the opposite choice from their own, viewing it as "wrong" (or worse) rather than just a difference in what one chooses to designate by the word "mood".
My own opinion is that it's nicer to limit "mood" to the different kinds of predication (declarative, imperative, interrogative, etc.) and treat the infinitive as sui generis. I think most grammarians today share this opinion, both traditional grammarians (the great majority) and those devoted to CGEL. So, if you omit the infinitive from lists of moods, you'll probably stay out of trouble.