iPhone 5s LED Flash and buttons not working

Well if you're a tech and know how to open up your phone you can do that

As you mentioned that only home button is working you probably can't do hard reset(home + lock button)

You can try to disconnect the battery and re-attach it after a few sec to see maybe this will bring back your buttons

Otherwise you might try to change flex cable where all the buttons and a flash are located

There should be a guide on this website if you never had done it, but if you're not a tech i would leave it for someone else as it's not the easiest task!