Here's the conversion formula:
T2 = T1* (D1 / D2) ^ 1.06
Example: Convert from 4K to 5K for someone who ran 15:30.
Step 1: Convert the 4K time into minutes or seconds. 15 + 30/60 = 15.5 minutes.
Step 2: Plug & Chug
5K time = 15.5 * (5000/4000)^1.06
5K time = 19.63 minutes or 19:38
You can use this formula for distances that are reasonably close, i.e. 4K to 5K. However, you can't use it to project big differences in distance, e.g. 5K to 1/2 marathon.
I used this same formula to convert my the times to 5K efforts from my old high school team pre-1980 when the distance was only 2 1/2 miles. The result was a physical confrontation with an overly zealous parent. He didn't like the fact that his kid wasn't nearly as good as he thought he was.
Let's just say my team would have had 7 guys sub-17:00. :^)