Q. In a number of benchers, I’ve seen printed that there’s actually a 5th verse/stanza to Sholom Alechaim. Why is the minhag not to sing/say this verse?

A. In a number of Sephardic sidurim there is an added verse between the common third and fourth that begins with “Beshivtechem Leshalom Malachei Hashalom – When you seat in peace, angels of peace” (Sidur Otzar Hatefilos – Iyun Tefila, Sidur Tefila Hechadash – Sepharad, Vina 1922, Noam Shabbos p. 50, Imrei Shem 2: 11, See Divrei Sholom p. 262 as to the nusach of the Chida).
Mevasseres Tzion (33: p. 102) explains that the ones who omit it, is because they consider wrong asking the angels to sit, since they usually only stand. (Although the angels that visited Avraham Avinu, seemed to have reclined under a tree, they could have been different since they adopted a human body and also ate)
There are different traditions and minhagim in regards to all everyday tefilos in general as well as to what is recited during Shabbos and Yom Tov. Sholom aleichem is based on the saying of the Talmud (Shabbos 119b) that two serving angels accompany the one who returns to his house from the beis haknessess on Shabbos night etc. and we are to welcome them to our abode. Chasam Sofer omitted altogether reciting sholom aleichem, since today we do not have angels that constantly escort us. (Minhagim Ch. S. 5: 6), this is also the opinion of Hagr’a. While others refrained from saying it, since they considered improper to ask angels to bless us, as it could be misunderstood as praying to them. (Pachad Yitzchok- Tzadik 33b).
The Ya’avetz (2: 125) and others excepted because of the custom to abstain from asking for one needs on Shabbos. It is said that the Chofetz Chaim would also omit singing sholom aleichem when guest were present, in order not to delay and begin the meal as soon as possible in case the guest were hungry. However, most of the communities do sing or recite sholom aleichem.
Horav Shlomo Miller’s Shlit’a pointed out that in Lakewood Yeshiva they follow the opinion of the Hagr’a and do not recite sholom aleichem.. He also explained why on the first verse we name the angels “malachei hashores” or serving angels and then we change title and call them “malachei hasholom” or angels of peace. The reason being that since the angels witnessed that he is observing properly the Shabbos, both angels concur and are at peace with each other and proceed to bless their host with sholom. The Rov’s opinion is also, that one should always follow the minhagim and traditions of his family or the community to which he belongs.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a