Help: hard starting

I have a 2002 Mazda Protege. I bought a brand new battery a few months ago, so that isn't a problem. I also installed new spark plugs.
The car has trouble starting, especially when it is really cold out. I turn it over for 4-5 seconds before it finally, slowly, kicks in. When it is extremely cold out, it just doesn't start (remember I have a brand new battery). What do I have to do to fix this? I just want it to start normally.

I really appreciate any help guys
 
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