Will my pc run Skyrim smooth?

unfortunately no, have you got a console? might as well just get skyrim on that as the graphicss are equvalent to skyrim on low/medium settings anyway and that is what you might barely be able to run it on, sure the console version doesn't have mod support but too many mods would just slow down your frame rate further.

I have the Radeon HD 4650 card and I have no problems playing Skyrim with a couple mods.

Sorry buddy.

http://community.futuremark.com/hardware/gpu/ATI+Radeon+HD+5450/games

http://www.videocardbenchmark.net/gpu.php?gpu=Radeon+HD+5450

It may be possible at 800x600 resolution with lowest settings, no shadows, and the low-res texture pack. Possibly you'll get a tolerable fps.
This laptop has i3 2.4GHz with Intel HD Graphics 1st-gen and it can just barely manage Skyrim with the setup I described.
I've finished Dawnguard as well, and have loads of mods installed. It doesn't look awesome but it's playable and I've exhausted interest after 267 hours.

That's assuming my gpu is worse than yours, and I don't know that. Good luck.

This is my Skyrimprefs.ini http://pastebin.com/dYi7dVAz

Hurr Durr

Yes, I'm running on a Pentium processor with Integrated Intel Graphics, 3gb RAM, 750gb 7200rpm HDD, with fairly decent gameplay. It's slightly lower in certain areas, and sometimes unbearable in certain areas of the Thieves Guild and other places with lots of clutter. But I think your PC should run it... I'm running on low graphics though...