My Apple Watch 5 screen has turned black , I have tried pressing both buttons simultaneously couple of time even on the charger but still no success , my watch seems alive but no screen

If you tried all the steps in:

If your Apple Watch won't charge or it won't turn on - Apple Support

then it may be a hardware problem. For repair & service:

watch Repair - Official Apple Support

watch Service Pricing - Apple Support

If you still need help, contact Apple Support.

I went through 6 series 5 watches and 1 series 6 watch due to the same problem. Now my replacement series 6 watch is having display problems. Unfortunately the series 5 and 6 Apple Watches have serious issues and are junk!

At least they are giving you a replacement. My Apple Watch series 6 display turns off in sunlight but is still responsive even though the screen is black. Been on phone calls with apple support for 2 months and refuse to replace it as it "might" be a software issue and are scared that the replacement they send will have the same issue.