Unfortunately the HP_Recovery partition is not the one with your data. The HP_Recovery partition is where the original setup for your HP is stored, in case you ever needed to Restore the laptop to factory conditions.
There should have been a 2nd Volume that mounted, but if not, then open disk utility
Applications>>Utilities>>Disk Utility
In the left pane, look for the HP_Recovery partition to be listed, and see if there is a 2nd partition under or above it that is greyed out. If so, right click on it (CTRL+click if no right click is available) and select Mount from the option menu.
See if the Volume mounts to the desktop now. You should be able to Read from the Volume (I imagine it's NTFS) but won't be able to write to it without 3rd party software.
The Recovery Partition probably automounted because they are usually formatted in Fat32 (A DOS format that Mac can read and write to).
Hope this helps,