How come when I turn on my computer it goes to black screen that says [F5] key for HDD recovery?

go into safe mode , I think you hit either F5 or F8 during start up. You want safe mode with networking perhaps. From safe mode attempt a recovery to an earlier date when your machine was working.
GOOD LUCK

If you're running Windows XP and Windows crashes or becomes unusable, you may have to run a Windows XP recovery setup disk to make your computer usable again. When purchased, many computers don't come with a Windows XP recovery setup disk, but you can download one for free from Microsoft. The Windows XP recovery setup disk holds the computer software and files that you need to assist you in rebuilding your operating system.

Place a formatted floppy disk in your floppy disk drive. You will need six formatted floppy disks. Visit Microsoft's Download Center and download the version of the setup disk for your version of Windows (see links in Resources). http://www.microsoft.com/downloads/details.aspx?displaylang=en&FamilyID=E8FE6868-6E4F-471C-B455-BD5AFEE126D8 Home Edition http://www.microsoft.com/download/en/details.aspx?displaylang=en&id=8030 Professional Edition set up disks for floppy http://www.download3000.com/download_17676.html XP Recovery CD Maker Windows XP Home Edition and Windows XP Professional Edition have their own recovery setup disks and you must use the correct disk for your version of Windows. Click "Download" and then "Save." Find your floppy drive or optical media drive on the menu and click "OK." If Windows isn't functioning at all, you will have to perform these actions from a working PC. Remove the last floppy disk when the Windows XP recovery disk download is complete and place it in the computer on which you need to use it. Shut down your computer and then turn it back on. If your computer prompts you to boot from the disk, press Enter. If it doesn't, you'll have to go into your BIOS to set the computer to boot first from your disk drive. When your computer boots from disk it will automatically start running the Windows XP recovery setup disk from which you can then set up Windows XP. Hope this helps.

Use the Bootcfg utility in the Recovery Console to correct the Boot.ini file:

1. Use the Windows XP CD-ROM to start your computer.
2. When you receive the message to press R to repair Windows by using the Recovery Console, press the R key.
3. Select the Windows installation that you want, and then type the administrator password when prompted.
4. Type bootcfg /rebuild, and then press ENTER.
5. When the Windows installation is located, the following instructions are displayed: Add installation to boot list? (Yes/No/All)
   [Type Y in response to this message.]
   
   Enter Load Identifier:
   [This is the name of the operating system. Type Windows XP Professional or Windows XP Home Edition.]
   
   Enter OS Load options:
   [Leave this field blank, and then press ENTER]. After you perform the preceding steps, restart the computer, and then select the first item on the boot menu. This should allow Windows XP to start normally.
   
   After Windows XP has successfully loaded, the Boot.ini can be modified to remove the incorrect entry.

do u get any error message on bottom of blue screen?
Try safe mode using f8

If you don't see the message on start up "Press any key to boot from cd" Then you need to change the boot order.

Start the PC and hit delete a number of times. This will take you into the bios screen. (Set up screen)

You will have a tab called "Boot Priority" or "Boot order". Make sure that CD/DVD drive has 1st priority. Save & exit & your done. Upon restart if you have a disc in the drive you will get the option to press any key to boot from CD/DVD. By default, most motherboards are set to boot from floppy & then Hard drive so in most cases you will need to enter setup & change the boot order.

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Hell, Sorry to hear your having problems your analysis sounds correct but lets make sure it's not something else first. Can you give me more details on the drive Brand, IDE/SCSI, model number. Do you have access to a computer with a CD burner?

I have just in fact a few days ago came across a similar issue. As to whether or not your hdd needs to be replaced is uncertain. What I can tell you is it seems as though the MBR or master boot record has become corrupt or one of the reader arms inside the hdd has failed.
Refering to the corrupted theory, may be simply fixed by booting off of a win xp cd and reformatting your drive and reinstalling windows after the format.

HOWEVER

In my case even booting off of a xp cd did not resolve the issue, every time anything would attempt to read from the hdd the computer would reboot. I suspected hdd failure at first, but this was not the case. It turns out it was a virus that infected the ntfs.sys and the MBR and put a binary code into those 2 files to reboot the machine.

Luckily at work (IT industry) I have a norton ghost server and was successfull at reimageing the hdd, doing so erases the MBR and everything else for that matter and rewrites it. However in doing so I lost all data that was on the hdd to begin with.

If you are not very tech savvy I would probably recommend hdd replacement however since you do have a HP which was prebuilt with xp, you don't have a xp install cd and thus unable to reload windows. I recommend finding a friend that has the xp install cd or you will have to go to the store and buy XP.

Replace the HDD.
You don't want your precious data on that drive.

Try first  to use hiden boot cd.With it u can see all files on hdd.When u see winxp files just delte.But i will not take responsibility couse sometimes xp wont boot up...
 
But i recomneded you to save all your data and format your pc.Make sure that the partition cd must be deltet befor u contiuing with formating ur pc like in this pics:
 
http://www.imagehost.ro/pict/3003390347268b3728923.jpg

I believe you should select the top MICROSOFT XP HOME EDITION line as the newer versions of Windows "instances" are placed on top.