Could we have a clock speed on your CPU? Not that it won't handle Skyrim, but it would be nice to have that rather important figure.
The clock speed on a i5 2400 is 3.1GHz [Turbo 3.4GHz]
FYI:
i5 2300 - 2.8-3.1, locked multi
i5 2500 - 3.3-3.7, same
i5 2500 - same, unlocked multi.
i7 2600 - 3.4 - 3.8, locked,
i7 2600k - Same, unlocked
...in truth though, clock speed doesn't really matter if the CPU is an i5 or i7, you can assume it will plow through Skyrim pretty well as they all turboboost. My laptop i7 starts at 1.6GHz and it plows pretty much everything.
As for i3 CPUs, they don't have turboboost, but the lowest Desktop is 2.5GHz and will surely run Skyrim... so they won't be an issue. Only the bottom half of i3 mobile processors and the i5 430UM should be where a problem starts with the "i" series.