I am trying to print a greeting card!

Before printing you need to select the size and orientation and it's a good idea to look at the preview before printing. That saves a lot of paper.

no,
there is no way to print on greeting card.
use century paper to print then make greeting card.

This could be due to the print-head clogging up, or your ink cartridges being low.
First, I would suggest cleaning the printhead.

Setup menu -> Tools -> Clean Cartridges

Then try it once again. If this doesn't work, try cleaning the print head manually, as per this guide.

http://www.ifixit.com/Guide/Repair/HP-Photosmart-Premium-Maintenance/3515/1

If the problem persists, buy new cartridges.

toner drum is faulty replace it

Check to see if you are feeding the envelopes and 4x6 cards/photo paper correctly.

Both envelopes and 4x6 cards must be loaded and centered on the paper exit tray (not inside the paper input tray).

Printing envelopes:

• Up to 15 envelopes can be loaded at a time.
• The print side of the envelope faces down.
• The envelopesare centered on the paper exit tray.
• You print the envelopes with Landscape orientation.

Printing cards:

• Up to 35 greeting cards, index cards, postcards, or photo cardscan be loaded at a time.
  
• The print side of the cards faces down.
• The cards are centered on the paper exit tray.
• You select Automatic, Normal, or Photo print quality.

For images on how to correctly load the paper, download your printer user's guide:
http://support.dell.com/support/edocs/systems/prn946/en/index.htm

Hasn there is a roller which help the page or card to move into printer which if use frequently get so smooth that the page is not printed out instead get jam try getting printer service and replacing with New Roller.. if you don't understand any thing regarding ... ask me

Centre the paper tray guides. However as the papersize is quite small, the guides may not be close enough to maintain the paper in the centre.
You can either cut the paper a little bigger so as to match the tray guides and then trim the excess paper after printing.

Or you can place two pieces of cardboard or any other material of same thickness on either side of the paper so as to center the paper with the sides of the tray.

it now requires a general servicing so kindly contact the manufacturer or service center

Yes and no. Unless you have a printer that prints on two sides you will have to "trick" it and use the template for both. Make a front and a back. You will have to print one one side then inset it to print on the other side. Since all printers feed difrently you will have to play with this on scrap first before using your good card stock. For example I made invitations to a wedding. The couple wanted a pcture on the fornt. On my template I had to rotate the picture upside down so when it was folded in half the picture wa right side up. It also had a raised rose on the invitations so I had to adjust the image so it would print in the empty are on the front. I then had to do the inside text and makes sure the paper was inserted correctly as not to print upside down. You can do it but it is tricky, that is why I recommend some scrap paper first. Good Luck.

At the moment it is printing both sides of Greetings cards, but this printer appears to be very sensitive with regards to placng card in the exact position in the paper tray.

Why it will not print envelopes without smudging I still don't know, so I shall just have to write address by hand after I place graphic on the envelope

This 5300 was a Christmas gift from my wife and if I could afford to change it I would. The performance is very dissapointing

Kindest Regards
David Gray