In order to reach the bottom right corner from top left corner, you have to travel through 5 rows and 5 columns. You can observe that whatever path you take, in every path you would be going through 5 rows and 5 columns.

So now say you have the rows numbered as R1 R2 R3 R4 R5

and columns numbered as C1 C2 C3 C4 C5

Now how many ways you can arrange the rows and columns so that relative ordering is maintained, i.e. R1 should be followed by R2, R2 should be followed by R3 and so on…

so it’s equal to = Total arrangements/Restricted Arrangements

= Total Arrangements/(Row Restrictions)*(Column Restrictions)

=10!/5!*5!