I know that basically, the first
6 5 books in Christian's Bible forms the Torah. However are there any subtle difference between torah and those books?
The first five books of the Bible -- Genesis Exodus Leviticus Numbers Deuteronomy -- form the "Torah" (like would be in a Torah scroll). The text of these is, as far as I know, identical between Jewish and Christian Bibles (though there will certainly be differences in translation; studying the original Hebrew is extremely common for Jews, but rare for most Christians).
It's the next set of books of the Bible that are a bit different between the Jewish Tanach and Christian "Old Testament." See Wikipedia for more. Some books are ordered differently (such as what comes after Judges?); some are in one canon but not the other (such as Ecclesiasticus); and some are counted as single/multiple books differently (e.g. The Jewish Bible counts Samuel I & II as one book, and Ezra & Nechemiah as one book).
There are sometimes also differences in chapter/verse numeration. For example, Gen. 31:55 in the KJV is 32:1 in (most if not all) printed Hebrew Tanachs, so the numbering of all of the verses in ch. 32 is one off. Similarly, in Ex. 20 (the Ten Commandments) the KJV divides and numbers each of Commandments 6-9 as a separate verse (paralleling the way it's done in the public Torah reading, called Taam Elyon), whereas printed Tanachs follow the verse structure used for private reading (Taam Tachton) and combine all of them into one verse.
(Note that this doesn't apply to Torah scrolls; those don't have chapter or verse markings at all, since they are a medieval invention.)