ABRSM grade 5 theory is in fact very important, especially if u wanna continue to higher grades. without this, u wont be allowed to move on to the next stage.
so yes, must take grade5 theory first if u wanna continue.

if not mistaken, the other one is guildhall, but it is now joined with the trinity board, so currently there are 2 examination boards :

i)ABRSM
ii)Trinity Guildhall Examination.
owh and Yamaha Higher Grade Examination too, if ur learning at Yamaha.

Most people would usually finish their ABRSM grade 8, then continue with trinity for diploma, im not sure why, but yea my piano teacher once told me that the ABRSM syllabus is generally harder than the Trinity's.

its your choice actually, but both are equally recognised.

if u wanna get a diploma, find a teacher who teaches diploma, then go for the exam..

some people start teaching.. some further study to get a degree or higher in uni.. some just stop there because they wanna study something else..
it reli depends on which route u wanna take..