My Hebrew Birthdate(?)

I'm working on getting the correct date, though I have the date of 26 Tevet 5770 (really, 26 Tevet 5769). I was born on January 23, 1990, and I downloaded the Israeli New Moon Society archive table to find if January 1990 and Tevet 5749 coincided at all. Only three dates were listed for 1990, and none of them were in January of 1990. So, I wasn't going to find out what January 23, 1990 was.

I have been able to learn and observe, however, that the Biblical calendar (which factors in the Aviv Barley) and the P'rushi calendar coincide to some extent (and they actually sometimes exactly coincide. This month of Tevet 5774/"5775", they did not exactly coincide. I originally thought that they did, though I guess that I was tracking it on my own copy of the P'rushi calendar and put "Tevet 1 if not earlier.". I thought that my copy put Tevet 1 on December 23rd or 24th.).

So, then, here's what I've been able to calculate:

1. I originally thought that my Hebrew birthday was on January 18, 2015 at sundown.
2. I went back and looked at a moon-phases calendar (I originally tried the one from the Israeli New Moon Society. It didn't download.).
3. I looked at the traditional Hebrew date again.
4. I looked at the traditional start of Tevet 5749/"5750" (December 28, 1989. On December 29, 1989, it was the day of Tevet 1, 5749; since Hebrew days are evening-and-morning days.).
5. I saw that the New Moon was actually on December 29, 1989. 
6. So, then, began the count.
7. The conclusion....

I was born on Tevet 25, 5749. Thus, I will be 25 on....today. Well, Happy Birthday to me and a Peaceful Sabbath to all (ליום הולדת שמח ללי ושבת שלום לכולם.). Meanwhile, I took a while to calculate this since math is not my strongsuit.