What did the Buddha mean in AN 5.38 with the fifth benefit to a person of faith?
You can find the Pali words on Sutta Central:

...  saddho kāyassa bhedā paraṁ maraṇā sugatiṁ saggaṁ lokaṁ upapajjati ...

To answer your question, I think the text has been correctly translated. The translated word “breaks”  corresponds to &quot;bhedā&quot;. For this context see notes from the PTS:

&quot;Abl. bhedā after the destruction or dissolution in phrase kāyassa bhedā param maraṇā, i.e. after the breaking up of the body &amp; after death: see kāya I. e. &amp; cp. D. III, 52, 146 sq. , 258; Dh. 140; Pug. 51&quot;

The other words roughly correspond to paraṁ=after, maraṇā=death, sugatiṃ=good (destination), saggaṃ and lokaṃ can be taken indepently but together they roughly translation to &quot;heavenly region&quot;, upapajjati=reborn.
Again see notes for uppajjati in relation to saggaṁ and lokaṁ:

Upapajjati, (doubtful whether a legitimate form as upa + pad or a diaeretic form of uppajjati = ud + pad. In this case all passages ought to go under the latter. Trenckner however (Notes 77) defends upa° &amp; considers in many cases upp° a substitution for upa. The diaeresis may be due to metre, as nearly all forms are found in poetry. The v. l. upp° is apparently frequent; but it is almost impossible to distinguish between upap° and upp° in the Sinhalese writing, and either the scribe or the reader may mistake one for the other) to get to, be reborn in (Acc.); to originate, rise Vin. III, 20 (nirayaṃ); A. III, 415; V, 292 sq.; Sn. 584; It. 13 (nirayaṃ), 14 (sugatiṃ; v. l. upp°), 67 (saggaṃ lokaṃ; v. l. upp°); ...
PTS

A similar verse occurs in the Dhammapada:

atha vassa agarani aggi dahati pavako
kayassa bheda duppabbo nirayaj so 'papajjati
(DhP 140)
...
bheda: bheda-, N.m.: breaking, disunion. Abl.Sg. = bheda.
The phrase kayassa bheda- (&quot;disunion of the body&quot;) means &quot;death&quot; in the Pali texts. 
source