I have a Lenovo Thinkpad Edge 11 0328CTO (intel HM55 chipset) that came with a i3 380UM, which is a low power 11W processor. I wonder if i can upgrade that to a i5 430M, which is the same socket, but is 35W tdp.
You can upgrade your processor to i5 430M on the Intel HM55 Chipset which you have. Here is a confirmation of the chipset working well with i3/i5/i7 processors.
Make sure you get it done by a professional or have a look at something like this.
For other safety factors, just check your passive cooling system and check your PSU if has the capacity to give an output with extra power. Because your motherboard definitely supports a power change. Most laptop vendors design their hardware for flexibility.