a challenging situation of asking for a letter of recommendation

I am currently applying to Ph.D. programs at several universities. Since I was a transfer student in my undergraduate years, and I have great relationships with my professors at community college, I asked them to be my letter writers for letter of recommendations.

Today I received an email from one of the schools I am applying to asking for a LOR from a professor from the school that I got my bachelor degree (or else they are likely to reject my application). They give me time until mid January to turn that in.

My problems now are: 1. I graduated five years ago and have not contacted my professors there 2. I contacted their departments today to find out their office hours but they are gone for winter breaks already.

It seems like that my only option is to just email them. And my thoughts are that the worse case scenario is just a "no" from them. And as long as I am being polite, I would not be blacklisted (please correct me if I am wrong on this).

If that is the case,should I be straight forward in my email explaining my situation honestly and ask them if they could write me a LOR or since I have until mid January, just ask them for a LOR as I would normally do it?

I drafted the two version. Any comments or feedback will be helpful. Or if none of my solutions are a good one, I would really appreciate a better solution.

Thank you very much!

============ First version

Dear Dr. Smith,

This is Mary, I took your XYZ class back in 2010. I apologize for my presumptuous email. I was on campus today but found out there is no class this week. I was hoping to ask you in person to see if you would be willing to write me a letter of recommendation.

I was majoring in ABC and I am currently applying to CDF. (and I plan to give some more background info)

You are the best person to write me a letter because not only did I gotten an A+ in your XYZ class and you made great comments about my group project on WHATEVER, your class was also the class that raised my awareness in XXX. I have my statement of purpose, transcripts, curriculum vita ready, which I will be able to provide.

=============== 2nd version

Dear Dr. Smith,

This is Mary, I took your XYZ class back in 2010. I apologize for my presumptuous email. I was on campus today but found out there is no class this week. I was hoping to ask you in person to see if you would be willing to write me a letter of recommendation.

I was majoring in ABC and I am currently applying to CDF programs. I have submitted my application to University of 123. They said they need a letter of recommendation from my University 321 professor. If not they will likely to reject my application. They gave me a deadline to turn in this letter of recommendation by January 10th, 2015. Would you be willing to write me a letter of recommendation? I have my statement of purpose, transcripts, curriculum vita ready that I will be able to provide.

You are the best person to write me a letter because not only did I gotten an A+ in your XYZ class and you made great comments about my group project on WHATEVER, your class was also the class that raised my awareness in XXX. I have my statement of purpose, transcripts, curriculum vita ready, which I will be able to provide.