I tried and can download the latest version of the xamarin studio (i.e. 5.7.2) from the account, but I cannot find any option for xamarin studio 5.8. I am looking for xamarin studio 5.8 download link.
Windows or OSX? You should be able to download via the updates menu inside of Xamarin Studio itself. Here is the hard link: http://download.xamarin.com/studio/Mac/XamarinStudio-5.8.0.443-0.dmg.
Maybe they just updated the site? I checked my install files on my subscription page and it is there in the dropdown list.