Today I was trying to pump my bike tire using mini pump. It has presta valve and after pumping i found that I've bent the valve core by about 5 to 8 degree angle. I tried to bend it back enough for it to be somewhat straight. My question is, should I replace the core? Should I be worried?
It happens, especially if you remove the pump head not perfectly vertically or you move the pump head while pumping.
or bracing the head of the pump while pumping.
Its not the end of the world if the valve core is bent -- I've run tubes for years with slightly bent valve cores. Note that at some point it may break (and you'd need to get a new tube then). The presta valve only lets out air when you press down on the valve core, which you can't do once you tighten down the nut (even if it doesn't sit flush with the rest of the valve and hits the stem at the angle, you can't push the nut down anyway to let out air).
I wouldn't worry about it. Repeatedly bending the core could cause it to break, but as a one-off, it should be fine. I quite often end up with slightly bent cores, and don't normally bother bending them back, and I don't recall ever having a valve fail.
At some point when you replace the tube, get one with a shorter valve. Prestas come in different lengths to accommodate different rims and some (like for aero tires) are way too long. A larger bike vendor will have a better selection of sizes.