Who cares if you're a 'slow' runner? You're out, doing it.
Nailed it.... but, I get it. Everyone wants to go faster.
I'm a "faster" runner, but the same things that hold true for me also hold true for you, and even Meb Keflezighi (American elite marathoner).
but first: If you can do two miles, you CAN do a 5k RIGHT NOW. So, if you think you aren't there, yet, or you're not ready... You Are. Thinking you're not is just something you're telling yourself because you haven't proven it to yourself, yet.
Now, Getting faster:
This will come with consistency and volume, and perhaps some more weight loss (but that isn't necessarily necessary).
You get better and faster at running by running more. It's just that simple.
After every triathlon season, I would take a good amount of time off, and when I did, it invariably turned into a couple of months of being sedentary. During this time, my fitness levels would drop like crazy. When I would come back, I'd be running 12-13 minute miles for an effort level that would normally have me doing sub-8 minute miles when I was in peak shape. Don't get hung up on those paces, but DO pay attention to the difference there.... and the fact that with just 6-10 weeks of consistently getting back at it, I would almost completely reverse that gap. You may never realize that same degree of variance, but you WILL see a significant change with consistency and increased volume. You have to build slowly and give yourself time to adjust, though, especially us older athletes, so we can avoid injury.
If you are currently doing 2 miles twice a week, add a third day. If you're not at twice a week, then add a second day and the following week add the third day.
Spread them out over the week so that you have at least one rest day between each run (e.g. Mon-Wed-Fri). Recovery is SUPER important.... as important as sleep and hydration.
This is your baseline. 2 miles, at an appropriate effort level, three times per week. Literally, just doing this from now until spring will not only have you going faster, but it will guarantee you will be able to do that 5k.
BUT, let's get you a little better prepared:
Give yourself three weeks to get acclimated to going out three days a week, and then push one of those days up to 2.5 or 3 miles. You should prefer 3, but stick to 2.5 if you're not sure you can do that extra half mile.
Give yourself two weeks to get acclimated to that, then push a second day up to 2.5 or 3 miles.
Give yourself two more weeks to get acclimated and push that third day to 3 miles. no option for 2.5 here, jump right to 3... by the time you're bumping this day up, you're ready for it.
Do NOT worry about pace; focus on level of exertion. If you have a way to monitor your heart rate (e.g. a smart watch or some other device) simply wear it during every run and just glance at it occasionally during your run to ensure you are in your Aerobic Zone. You can go a little higher, but not too high and don't let it fall lower than Aerobic at all.
If you do NOT have any sort of heart rate monitor, then you have to learn to rely on Rate of Perceived Exertion. It is far less accurate when you're newer because you won't be as in-tune with your body, but in time you can do just fine with it. The best rule of thumb here is that you should be moving at a "conversational" pace. You should not be breathing so hard that you can't talk. If that means that you move at nothing but a brisk walk for now, then so be it. It will correct itself in time; you need to build your aerobic capacity and that only happens by getting your body to realize that you really mean to do this regularly so that it triggers the adaptations to make it easier on you.
Simply doing this you WILL get faster. At this stage, you are running 8-9 miles per week in your aerobic zone with your long run at 3 miles and you are 7-8 weeks into it.... By nothing more than remaining consistent with this (this means getting out and doing it even when you don't want to or when the weather kinda sucks) and it having a decent volume, your body WILL adapt and you will find in time (around the 6 to 10 week mark is when I've usually begun to really notice it) that you have to move at a faster pace to keep the same heart rate during your runs. And that there's the key.... go by heart rate and NOT pace. Your heart rate does not lie to you, it is the true measure of the work your body is doing; it also will keep you honest and putting out effort on the days you maybe don't really feel like doing it, and it'll keep you from going too hard on the days you feel good, too... and, as you gain fitness you will automagically be moving at a faster pace to maintain the same heart rate.
If you want to add more mileage after this, just follow the pattern above of increasing the distance of a single day, then giving yourself time to adapt. However, for your current goals, you totally wouldn't need to.
The unnecessary note on additional weight loss: carrying excess weight does slow you down. When I was younger, the rule of thumb I was taught was that every extra pound of body weight you are carrying adds 2 seconds per mile to your run pace for the same effort exerted.... what this would translate to here is for the same heart rate, you'd be 20 seconds per mile slower if you put on 10 pounds. The modern rule of thumb appears to be more like 1.4 seconds per mile, but I still lean on the 2 second rule. So, if you still have additional weight you're planning to drop, there is some free speed in there.
A Note on treadmills: If you are doing all of your running on a treadmill, as many of us tend to do up north in winter, then if your treadmill supports it, add 0.5 to 1.0 degree of incline to the treadmill. This will offset the help you're getting from the treadmill's motor and it will feel more like running outdoors.... and you'll be better prepared to return to outdoor running when the weather breaks.
