Another limitation posted in the specifications is that the largest memory modules you can use are 256 MB.
"Accepts 8, 16, 32, 64, 128, and 256 MB SDRAM modules in any combination"
Many laptops were designed for specific memory modules. You need to match the voltage and memory density for any new memory you install.
I had very good luck with Memory Up providing the correct memory I needed to max out an older Toshiba laptop. While higher than the cheapest price I could find for the base memory type, the DIMMs from Memory Up actually worked with the laptop first try.
From the Memory Up page for Solo 5300:
"Your Gateway Solo 5300 only supports memory modules made with a specific type of chip. Should you find what seems to be the exact same memory modules elsewhere for a lower price, it is very possible that the cheaper memory modules will not work in your system. By using Memory-Up's Memory Finder, your selected memory modules are Guaranteed To Work or your money back."
There may be other sources for proper memory modules for older laptops, but I have had success with Memory Up.
Chas