The 1874 RLDS edition replaced inherit with enter, but the 1908 RLDS edition restored the original inherit to the RLDS text. Either reading is possible: in the Book of Mormon, there are 12 examples referring to “the kingdom of God/heaven” that take the verb inherit and 4 that take enter (two of which are from the Sermon on the Mount as cited in 3 Nephi 12–14). In the New Testament, there are 6 references to “inheriting the kingdom” and 13 to “entering the kingdom”. The typesetter for the 1874 edition seems to have been influenced by the more frequent biblical use of enter in this context (in particular, the familiar usage from the Sermon on the Mount).
Summary: Maintain the verb inherit in Alma 5:51, the reading of the earliest textual sources; either inherit or enter is possible in the context of “the kingdom of God/heaven”.