I'm playing Bach French suite no.5 in G major BWV 816 for ATCL diploma exam. This suite was composed in Baroque period, so should I play staccato on each notes? Should I use a bit pedal? Because the piano still hasn't been invented in the Baroque period, and there was only harpsichord and clavichord, should I imitate their sound on the piano?
Certainly no need to play staccato. Opinions on pedal use in Baroque music differ.
One feature of the Baroque style was that the musical content was more important than the sonorities. Yes, Bach wrote for unaccompanied violin and cello making full use of their technical possibilities. But a whole lot more Baroque music was practically interchangable between keyboard, string ensemble, wind instruments - whatever was handy. And all those musicians would have played and phrased in the ways idiomatic to their instruments, they wouldn't have been obsessed with imitating a harpsicord!
So my take on it is - be aware of the history, serve the music as best you can, but don't worry TOO much about 'authenticity' unless you ARE playing music specifically intended for harpsicord ON a harpsicord.
Your teacher's opinion may differ. Listen to him too.
Baroque music consists of notes, not sound effects. A harpsichord by no means is the only keyboard instrument on which something might have been played. With regard to pedaling in an exam, you need to be quite careful: when there are countermelodies, in particular in stretto passages, the pedal cannot do multiple voices justice at once. Anything that will turn polyphony into one harmonized melody will get purists rather annoyed.
Doing staccato outside of the score demanding it would be a distraction: you need to make the best and most consistent of all your lines. That may involve playing some lines legato and others more leggiero, but that is a really tricky feat to pull off consistently. Doing it in an unobtrusive manner is beyond diploma level. Don't angle for it if you cannot pull it off convincingly.
If you don't have the skills yet to aurally follow and mould your various lines at the same time, a no-nonsense consistent articulation is your best bet.