If you want to win a 5k, walking is a great start, but will probably not get you there on its own.
Fast walking will help you build a strong base level of aerobic fitness. Your heart and lungs will develop and improve your capacity for running. After you build this base, your cardiovascular system needs to learn to function efficiently as you approach (or exceed) your Lactate Threshold. Your muscles need to develop enough power and speed to propel you to the front of the pack, and enough stamina to sustain the effort for the 5k distance. There is no better way to do this than to get out and run.
For a 5k, you will want to spend time training with intervals, sprints, strides, fartlek runs, and on hills. These will help you develop the power, leg turnover, and stamina you need to be competitive. If you keep these sessions focused and intense, you shouldn't need more than three a week. On the remaining days, you can mix it up with slower and longer runs, walking, cycling, yoga, and other light forms of exercise.
Since you mentioned wanting to run a marathon, keep in mind that competitive marathon training and 5k training are very different. If you focus on 5k training, prepare for a very different challenge if you attempt a marathon. If you train for a marathon, you won't necessarily have a very competitive 5k time.
A popular approach with many amateur and regionally-competive athletes is to train and race shorter distances earlier in the season (spring) and then use the summer months to prepare for a fall marathon. If you tried this approach you would probably find that your walking regimen would be far more helpful in marathon training than 5k training.
If you want to dig into the science behind this answer, or need specific training advice, here are a couple of great books on the subject: