Is it optional?
Go ji (ni)goro benkyoushimasu. (i will study at about five)
is it a matter of choise if use "ni" here, or it depends on situation?

Question

Is it optional?
Go ji (ni)goro benkyoushimasu. (i will study at about five)
is it a matter of choise if use "ni" here, or it depends on situation?

Answer

Using "goro" would mean "approximately" and "ni" would confirm that it's on five.

Go ji goro benkyoushimasu （５時頃勉強します。）＝I will study around five. 
Go ji ni benkyoushimasu  (５時に勉強します。）= I will study at five.

But in this sense, it would be more natural to say "Go ji kara benkyoushimasu （５時から勉強します。）" = I will study from five.