Recently I came across some lines and could not really understand what the "も" is doing in them.
Example:
私にクラスに鈴木さんという名の生徒が５人[も]{L}いるので驚いた。
vs
私にクラスに鈴木さんという名の生徒が５人[が]{L}いるので驚いた。
Thinking about "も" here as "even" or "also" in these examples don't really make sense to me here and I read in another post that it has a total affirmation usage but I can't quite grasp it.
Your second sentence:
私
にのクラスに鈴木さんという名の生徒が５人がいるので驚いた。
is not correct. You don't use two が's that way. You'd instead say:
私のクラスに鈴木さんという名の生徒が５人いるので驚いた。
"Numeral + counter", such as ５人, ２個, ３回 etc., can function adverbially. You'd use it like this:
生徒がいる。 There're students. → 生徒が５人いる。 There're five students.
りんごを食べる。 I eat apples. → りんごを３個食べる。 I eat three apples.
山田さんに会った。 I met Yamada-san. → 山田さんに３回会った。 I met Yamada-san three times.
も, used after a numeral and counter, means "as many as" "as much as". You'd use it this way:
生徒が５人もいる。 There're as many as five students.
りんごを３個も食べる。 I eat as many as three apples.
山田さんに３回も会った。 I met Yamada-san as many as three times.
So your first sentence:
私のクラスに鈴木さんという名の生徒が５人もいるので驚いた。
means "I was surprised because there were as many as five students named Suzuki in my class."
