The printer’s manuscript has anguishable while the 1830 edition reads unquenchable. Both are visually similar, and one of these is most likely a misreading of the other. Presumably Oliver Cowdery was the scribe for this part of 𝓞. Here he probably wrote unquenchable in 𝓞, but his initial u may have looked like an a, thus leading scribe 2 of 𝓟 to misread the word as anguishable. For discussion of Oliver’s difficulty with these two letters, a and u, see the discussion regarding the name Cumorah under Mormon 6:2.
There are two examples in the text of “an unquenchable fire” (Mosiah 2:38 and Alma 5:52) and two of “whose flames are unquenchable” (Jacob 6:10 and Mosiah 3:27). References to “unquenchable fire” are also found in the King James Bible (two times: Matthew 3:12 and Luke 3:17). On the other hand, there is no use of the word anguishable anywhere in the scriptures, although anguish does occur (11 times in the Book of Mormon and 17 times in the King James Bible). The Oxford English Dictionary does not recognize anguishable. Even if the word did exist, its use as a modifier of fire seems quite implausible.
There is a third possibility here, namely, the word unextinguishable (or the equivalent inextinguishable). The latter part of this word agrees with the last part of anguishable. This proposed alternative is, however, longer than either anguishable or unquenchable, making it less likely as the reading in 𝓞. Although the OED lists unextinguishable (and inextinguishable), there are no instances of the word extinguish (or any words deriving from it) in the Book of Mormon or in the King James Bible. It seems that here in Mormon 9:5 the original text read unquenchable.
Summary: Retain in Mormon 9:5 the noun phrase “unquenchable fire”, the reading of the 1830 edition, since this is the expression found elsewhere in the Book of Mormon and the King James Bible; the reading “anguishable fire” is highly implausible, nor is there much chance that the original text read “unextinguishable (or inextinguishable) fire”.