I think you should continue regardless.
I'm super slow and my best time to run 5ks is just over 40mins. But I've gone ahead with the 10k program anyway (week 12 this week!). And I discovered I can run 10+Kms when I gave myself enough time!
Once a week I go away from the program and do a "Fartlek" run. Apparently it's sweedish for speed play? Basically It's interval training (slow jog vs fast run) to get you running at a faster pace overall.
To do this I go right back to week 1 day 1. When the voice over says to run then I'll sprint and when it says to walk, then I'll go to a super slow jog. It kills and I want to give up and I feel sore the next day but I think it's been helping me run 5kms faster.