Most of the time when you place an unsupported processor on a board it won't even boot. The question that you are really asking is can the Intel® Pentium® E5300 work on a board that supported a Intel Pentium 4 or Intel Pentium D processor? The answer is no it can not. The Intel Pentium E5300 is only supported on 3 and 4 series chipsets while the latest chipset that the Intel Pentium 4 and Intel Pentium D were supported on was the 965 chipset.
Now if you have a 965 chipset based board and you wanted to upgrade to the Intel Core™ 2 Duo or Intel Core 2 Quad there is a little bit of room as long as they were 65nm processors. So you might be able to use the Intel Core 2 Duo E6700 or the Intel Core 2 Quad Q6600 but nothing later.
Looks like MSI has spent some time working to get support for some older Intel® Pentium® 4 and Intel Pentium D processors. So that would be a good for for you. So times a Motherboard Manufacturer may add support for additional processors if they use the same socket. Heck sometime they take away support for some processors that would be supported on the chipset. Since that is done after the fact of us selling them the chipset I dont have any referance to the supported processors for their boards.