Although there is no limit on age restriction, but to be honest...most athletes will be out of their prime once they hit mid 30s. Not a mental thing, but purely a physical thing. The human body starts to go into a decline: IE your body takes longer to recover, takes longer to build.
Starting your badminton career at 25...is a long shot if anything, not to be discouraging. But it does take many years of training to be competitive at the Olympic level.
Take some lessons, join some tournaments and see how you've progressed and re-assess you're progress.