First you need to check with your system manufacturer if you can upgrade the processor. Most of the time this should be possible.
I assume the Dell Dimension 5100C will have the Intel® 945G Express chipset, however there are many intel boards whcih has got the 945G Express chipset. From the following link you can check in the associated boards section and select one of the board with D945G one by one and check the range of processors that may be used on this type of chipset.
At this stage it is difficult to tell you exactly which processor will definitely be compatible with the system. You should be looking for LGA775, the system frequency (FSB), cache and BIOS requirements. However for bios requirements, you should contact your system manufacturer for more information.
Hope this is useful.