can my mac OS X 10.5.8 be updated to mountain lion

It depends on which model of Mac you have. Click here and read all three steps to the bottom.

(89312)

No because it does not have a Mac App Store (MAS). You would first need to update to Snow Leopard 10.6.8 to get the latest version of Snow and the MAS.

But there is no guarantee as we have no idea what Mac you have and whether it has the hardware to qualify for Lion or Mt Lion.

You really must update your profile details in order that people can help you.