An important thing to remember when it comes to web browsing on old machines, is that the web browser, as well as the OS, must be optimized in order to do tasks better.
Also, when it comes to hardware acceleration, the driver version of your graphics card matters. Not all the driver versions are actually supported by the web browser you are using and so it might default to software mode, consuming CPU.
On my 1.4Ghz Tualatin with 1,2GB of RAM, I use Mozilla Firefox 28 Beta 9 with several about:config optimizations and extensions in order to reduce load on RAM and CPU and using the machine for web browsing is quite good. Many sites scroll very fast and smooth with it. It's also important to say that my graphics card is a 6800GT, which is way faster than a FX5500 (I had it in the past, and personally I don't miss it). So if you begin to optimize the OS and the browser itself, as well as checking different driver versions to see which one runs better with your browser, you'll definitely see differences. By the way, I strongly recommend Firefox 28 Beta 9 as it's one of the oldest versions of Firefox that support the modern web, including HTML5, and it's not as bloated as later versions are.
PM me if you want, I can hand you my prefs.js files and my extensions list to use with FF 28 Beta 9 so you can check if it will make a difference on your machine. It used to run well back when I had a 1Ghz Coppermine and now runs even better with the Tualatin.
My Retro Daily Driver: Pentium !!!-S 1.7GHz | 3GB PC166 ECC SDRAM | Geforce 6800 Ultra 256MB | 128GB Lite-On SSD + 500GB WD Blue SSD | ESS Allegro PCI | Windows XP Professional SP3