hello. You are going to need to inspect the bearing and front seal on the front of the drum, and also the bearing ring for front support. The rear of the drum is supported by two rollers underneath. First of all, here is a parts diagram for your dryer. On this first one, you can see the bearing ring for front support. Part number 36. It will need to be inspected for wear.http://www.appliancepartspros.com/partsearch/model.aspx?model_id=5513301&diagram_id=28263302#d28263302
The next thing that I would inspect is the front bearing and seal, which is part number 38 in this diagram. It will need to be inspected also.http://www.appliancepartspros.com/partsearch/model.aspx?model_id=5513301&diagram_id=28129401#d28129401
When these things are worn, it can cause the drum to drop slightly and snag your clothes. In order to take a look at these things, your going to have to know how to disassemble your dryer.
You do this as follows;
Pull your dryer out from the wall to avoid hitting the wall when you raise the cabinet top. Lift the lint screen access cover and remove the two screws inside. Do not remove the actual lint screen before you remove the screws. Removing the lint screen first could lead to accidentally dropping the screws down the lint screen shaft and into the blower wheel.
If your older Whirlpool clothes dryer model has a kickplate, remove it first. You can either pop it off, or pry the kickplate off the interior spring catches. Depending on your model, you may have to use a putty knife to push in on the spring catch at the center of the top of the kickplate. With the kickplate removed, proceed to lift the cabinet top.
Use a putty knife, or some other thin and flat object to wedge in under the cabinet top. Your goal is to push each of the two interior spring catches back out of the way, thereby releasing the cabinet top. The spring catches are located one on the left side under the cabinet top and one on the right side under the cabinet top.
Loosen the two bottom screws securing the front panel to the unit. Do not remove them just yet. Locate the two screws at the inside top of the cabinet. They also help to secure the front panel to the dryer unit. Remove these two screws. Balance the front panel as best you can as you remove the two bottom screws that you have just loosened. Disconnect the wire leads connected to the door switch. Hold the dryer drum in place and remove the front panel of your dryer. Some models may have extra screws holding the front panel in place. If you are having difficulty removing the front panel, do a check for more screws.
Reassembling the entire unit is basically the disassembly process in reverse. Reattach the front panel of the dryer in the same manner you took it off. Make sure you reattach the wire leads to the door switch, and replace all of the screws that were earlier removed. http://www.repairclinic.com/PartDetail/Drum-Slide-or-Glide/3406129/2702?modelNumber=WED5300VW0#repairHelpVideoTabs
You will want to watch this. It will tell you how to replace the seal on the door.http://www.repairclinic.com/PartDetail/Drum-Support-Bearing/279441/2683?modelNumber=WED5300VW0
this will show you how to replace the ring seal on the drum.
These are so detailed, I think it's all that you'll need to complete job. These whirlpool dryers are not hard to work on once you know how to do it.
I really hope this helps you. I hope that everything you need is covered here.