will an 03 sportster seat fit an 05 sportster?
are they mounted differently?

I think if they are the same model they should.

Hello,
I wanted to give you my opinion about the seat fitting. I had a 2003 Harley Davidson 1200 Sportster, and I believe they changed the frame due to the rubber engine mounts. They also changed the oil tank on the right side of the frame. Yours is metal, and the 2004-2010 Sporster models is plastic. I hope this information is helpful to you.
James Bradley

Having just replaced the seat on my 2010 Sportster 48 I can only offer one bit of advice. Make sure you check the clearance under the seat.

In another forum I learned that some seat pans crush some of the electronics under the seat against the frame. I had never heard of this, but saw examples where folks had "dimpled" the pans or cut away a portion for clearance.

When I asked my mechanic about this condition, I was told that the factory had made changes back in 2009, and the condition did not exist now. (I had him check my bike, just in case. )

However, I'd have to ask, does your bike fall into this category, or does your replacement seat meet the new requirements? It only takes a moment to check, or to ask your service writer if your bike falls into this category.

Comfort or not, if your bike quits on the slab, it's a long walk to the next off-ramp.