のうち means something like "among these (things)". Is that close?
Yes, I think it's close.
However, the DeepL translation of the sentence is "I would like to visit your office on the following dates. Monday, July 5th, 2:00 p.m."
The translation of DeepL is correct in terms of the meaning of the whole sentence.
I can easily imagine there is a kind of communication via email like this:
From: person A to B
私は、以下の日程であれば事務所におりますので対応が可能です
・7月5日月曜日 14時~
・7月6日火曜日 16時~
・7月7日水曜日 13時~
And person B reply like this
From: person B to A
それでは、ご提示いただきました日程のうち、下記の通り貴所にお伺いしたく存じます。・7月5日月曜日 14時~
if I try to translate the whole original sentence as close as the original Japanese, it would be like this:
Then, I would like to choose the following date among the dates you offered me to visit your office. ・Monday, July 5th, 2:00 p.m
Here is a little explanation.
「それでは」 represents "the existence of context"
this word is close to "Then," in English. So if it were not a line in the middle of a conversation like an email, this word would not appear.
the meaning of 「ご提示いただきました日程」
「ご提示いただきました日程」is the polite way to say "the dates you offered me". This phrase can be separated like this:
ご提示いただきました(a polite way of "be offered")+日程(means "date")
So 「ご提示いただきました日程のうち、」 means like "among the dates you offered me".
the meaning of 「下記の通り貴所にお伺いしたく存じます。」
This means "I would like to visit your office on the following date."
if I separate this phrase roughly just for translation, it's like this:
下記の通り(means "as follows")+貴所に(means "to your office")+お伺いしたく存じます(very polite way of "I want to visit ~")
Sorry for the cluttered answer. If you can't understand what I'm saying because of my bad English, please ask me. I'll try to explain in other words.