Is it possible to use an Intel Core i5 processor on a Core 2 Duo motherboard?
Is the Core 2 Duo processor chip shape the same as the Core i5's?
Core 2 Duo uses LGA 775. Core i5 (depending on generation) uses LGA 1156, LGA 1366, or LGA 1155. The sockets are not interchangable.
It is absolutely and unequivocally impossible.
The Core 2 Duo CPUs have no memory controller. They use an FSB to communicate with the Northbridge, which contains the memory controller. The Core i5 CPUs have a built-in memory controller and interface with the motherboard through a completely different interface (DMI).
So on a motherboard for a Core 2 Duo, the memory is wired to the Northbridge. On a motherboard for a Core i5, the memory is wired to the CPU. There is no way.