Hopefully a 2005 is similar to a 2003. I did this on my 2003. Don't try to replace this core without reading my experience -- all the way to the end. I started by studying my Haynes repair manual. It included a warning I don't recall seeing in Haynes before: it's a big job -- consider getting professional help. After getting a $1000 quote from my mechanic, I decided to do it myself. Haynes did all of their work and instructions for a 2000 model -- I assumed the 2003 would be similar since there were no alternate instructions. Problem #1: plastic parts in the dash are extremely brittle from age. Many parts were already cracked and a number of attachment points and clips broke off during my disassembly. Once I got the dash out (an extraordinarily difficult process) I was ready to have the car towed to the junk yard when I saw what I was up against: the heater assembly is wedged behind a 2" diameter steel tube that extends from one side of the car to the other and has multiple components -- including the steering column supports, etc. welded to it. I was trying to figure out how I was going to tell my daughter (the owner of the car) that I had failed totally, when it suddenly hit me -- there is an easier way. Here's the good news. Read all the way to the end -- there's a punch line that's even better.
Instead of removing the core intact, I cut off the inlet and outlet pipes a couple of inches above the point where they turn upward from the core. (I used a Dremel) They must be cut short enough to pull the core out past the blower assembly. Cut a few more inches off of the remaining pipes still in the car. (yes, you know where this is leading!) Cut the pipes off of your brand new core (yes, that's kind of scary) in the same place you cut the old core -- or perhaps a little higher. Buy some heater hose (5/8" inside diam.) and cut it long enough to span the gap plus a couple of inches. Buy four hose clamps -- the ones that screw tight -- I started with the smallest ones that fit, but they leaked, so I replaced them with the next size up. ("Ideal" brand #5212v from Pep Boys) Well, you can figure out the rest. It worked great. The plastic retainer over the pipes will no longer fit. I broke mine in half (deliberately) and replaced the remaining screw with a much longer one. It holds everything in place very nicely.
Now for the surprise ending: All of this could have been done by removing only the glove box and the heater core cover trim. No kidding. In fact, after I discovered it was leaking, I practically re-did the entire repair with only the glove box removed.