Command_R not working on Macbook Pro

Hello..

I verified my Mackintosh HD ¨Disk Utility¨ since my computer is running extremely slow, and it said disk needed to be repaired:

¨This disk needs to be repaired using the Recovery HD. Restart your computer, holding down the Command key and the R key until you see the Apple logo. When the OS X Utilities window appears, choose Disk Utility.¨

Here is the description from the Log button in Disk Utility:

2013-06-23 12:26:21 +0200: Verifying volume “Macintosh HD”

2013-06-23 12:26:21 +0200: Starting verification tool:

2013-06-23 12:26:21 +0200: Checking file system2013-06-23 12:26:22 +0200: Performing live verification.

2013-06-23 12:26:22 +0200: Checking Journaled HFS Plus volume.

2013-06-23 12:26:22 +0200: Checking extents overflow file.

2013-06-23 12:26:22 +0200: Checking catalog file.

2013-06-23 12:30:22 +0200: Checking multi-linked files.

2013-06-23 12:30:22 +0200: Incorrect number of file hard links

2013-06-23 12:30:22 +0200: Checking catalog hierarchy.

2013-06-23 12:30:22 +0200: Checking extended attributes file.

2013-06-23 12:30:22 +0200: Checking volume bitmap.

2013-06-23 12:30:22 +0200: Volume bitmap needs minor repair for orphaned blocks

2013-06-23 12:30:22 +0200: Checking volume information.

2013-06-23 12:30:22 +0200: Invalid volume free block count

2013-06-23 12:30:22 +0200: (It should be 46690915 instead of 43944619)

2013-06-23 12:30:23 +0200: The volume Macintosh HD was found corrupt and needs to be repaired.

2013-06-23 12:30:23 +0200: Error: This disk needs to be repaired using the Recovery HD. Restart your computer, holding down the Command key and the R key until you see the Apple logo. When the OS X Utilities window appears, choose Disk Utility.2013-06-23 12:30:23 +0200:

2013-06-23 12:30:23 +0200: Disk Utility stopped verifying “Macintosh HD”: This disk needs to be repaired using the Recovery HD. Restart your computer, holding down the Command key and the R key until you see the Apple logo. When the OS X Utilities window appears, choose Disk Utility.

2013-06-23 12:30:23 +0200:

So if I click on Command + R... this windows pops up:

Anyone knows how I can sort this out?

Why is my computer so slow?

I have a MacBook Pro (15-inch, Mid 2009)

Processor 2.66 GHz Intel Core 2 Duo

Memory 4 GB 1067 MHz DDR3

Graphics NVIDIA GeForce 9400M 256 MB

Software OS X 10.8.4

I hope this information will help you get a better idea what the problem could be...

Thank you all in advance.