I’ve been cycling for 2 years but more as a workout than as a training. I get 15mph averages with the trailer and the kids and 17mpg on the cyclocross with 32mm tires and a very upright position. This is on a 45 minutes ride.
I started running on a threadmill just a month ago and have done 5km in 23:53 but typically do it closer to 28:00.
What can I expect as an improvement between now and 3-6 months?
Here is what you can expect.
23 years ago I ran 17:ish 5k’s with an occasional high 15:ish depending on the course.
Sat I ran a 22:02…So, you will get progressivly slower.
Seriously though, it all depends on how you train. I’m not training to run fast 5k’s anymore.
What to you want to run it in? Your progression depends on your GOAL and your desire to reach that goal.
This is a very difficult question to answer. Your gains are going to have a lot to do with the amount of run training you are putting in and the types of workouts you are doing. I would recommend adding in 1 interval run a week to start. When I started 5 years ago my I ran the 5k of my first sprint in a 28:00. I am now running a 19:30.
I saw a lot of gains in the beginning, but as I have progress it gets much harder to bring my time down.
Everyone is different.
“17mpg on the cyclocross with 32mm tires and a very upright position”
Check your oil, air filter, tire pressure, and get some premium gas. Cyclocross bikes shouldn’t use that much gas…heck, they shouldn’t use gas at all! 
Your rate of improvement depends on how fit you are now, how frequently and how much you run and if you will be losing weight or need to lose weight. You can improve a lot by just running frequently at a steady fairly easy pace. Your pace will increase at the same exertion level. Build up your running frequency by adding 30 min runs. I think you see more improvement by increasing your weekly running workload by increasing the frequency of runs rather than the duration. Once you see no more improvement then start increasing duration, then eventually intensity. Adding intervals to your workout when you are just starting out or are only running 2-3x a week greatly increases your chances of injury.
My own numbers are: Several years ago I took a year off running due to injury and came back able to run a 6 mile flat run at a 8:48 min/mile pace. After less than a year I could run the same run at just over a 7 min/mile pace at the same heart rate. This was running 4-5 days a week.
Breaking away from the typical “not enough information” response:
In 3-6 months you will be running a 5k at exactly 21:49
.