I have some personal experience with going from a 35 min 5k to a 29:11. The difference? A year's worth of training. My slower race times came when my longest training run was no more than 4 miles, and I was running only twice a week along with other tri training. My sub-30 came when I was mid-program marathon training when my long run was closer to 10-12 miles, and I was running about four times a week.
Like everyone else has said, if you give us an idea of what your current fitness level and training are like, we can be more helpful.