Just to address one of your points (BT has covered others) it seems the difference is the GPS measuring. I fully expect the Garmin to have been much more accurate, but I don't know for sure. None of them are perfect but my experience with Garmin is good.
Can you not use googlemaps to re-create your route to tell you how far your ran? Better websites include www.gb.mapometer.com/ and mapmyrun too - here you should be able to exactly recreate the route you ran (assuming you remember where you went!)
Where exactly have you got to? I'm not sure which app you have, but in my plan, in week 5, there is a maximum continuous run of 5mins, then 8 mins.
But in week 6, there's the really big jump up to 20 mins continuous run? I'm guessing that it is this big step that has got you! But whatever the situation, think if any of these might help, if you haven't tried already.
If possible, do the run with a friend - or better, with more than one friend - but you certainly can still achieve this running alone.
Choose a flat area. Try to avoid the heat of the day (perhaps you can forgive yourself from losing a bit of confidence if some of the recent hot/humid weather affected you)
Run slower than when you were running 5-8 minute stints. At this stage, it is the time running that counts, not the speed/distance.
If you've done 8 minutes successfully in the past, then before you set off, set the alarm on your phone to audibly ring after 8 minutes and again at 16 minutes.
Set off - with the target of completing 8 minutes. When the alarm rings, then mentally treat it as a new 8 minute run (which you know you can run).. and keep going. When the alarm rings again, you know you only have 4 minutes to go
Adjust the timings of alarms in a sensible way when you want to go further than 20 minutes
The couch to 5K is divided into 9 weeks, but what people often don't notice is the instruction that 9 weeks is the "minimum" that the programme should take, and that you should repeat weeks if/when you have a struggle.
I don't say this to be discouraging. Quite the reverse. You should not be disheartened by being unable to follow the "ideal" progression. It's common.
But your 5k race isn't going to wait... so try to get up to a continuous 25 minutes run - then for a few days before race day, don't do more than a 12 minute run, so you're fresh.
You'll have to find something inside you to drive yourself on - but unless you have an injury, I'm sure you can find a way to do this - . Good luck.