Hello! From what I understand, the i3-390m is an older processor that belongs to the first generation Intel Core family. The processor uses the PGA988 package and only supports Socket G1. As a result, the CPU options you can upgrade are very limited. Some compatible options may include other first-generation core processors such as the i5-580m or i7-640m. Before purchasing and replacing a CPU, check the compatibility of the mainboard and BIOS to ensure that the new CPU works properly. I hope this short answer is helpful!
This is a mobile version of the processor, which can be upgraded to i3-370m, i5-460\/580m, i7-620\/628m, etc., but it is not recommended to upgrade, because one is that these belong to the eliminated processor, and the second is the high upgrade cost
This is the motherboard of the hm55 chipset, socket for socket989rpga, you can upgrade the first generation i5 notebook processor, i7 is not recommended due to heat, compatibility issues. You can choose either i5560M or i5480M.