Flats and sharps as key signatures

As we've learned, a key signature with one sharp (F#) is the key of G. We know that the F# is the leading tone which raises 1/2 step to the tonic note. In the G Scale remember the notes G A B C D E F# leading into G. So if the key of G has 1 sharp and the key of D has 2 sharps (D E F# G A B C# leading into D) we see there's a pattern to this.
An easy way to remember sharps is this little saying: Fat Cows Go Down An Easy Bank.
An easy way to remember flats is: Be Earnest And Don't Get Cold Feet.

So when you run into a key signature with 5 sharps, you can say Fat Cows Go Down An (and stopping right there at 5 words of our saying, you'll know the A# is leading 1/2 step to the tonic, which is B, therefore 5 sharps is the key of B.

With flats, it's a slightly different formula. Say your music has 3 flats. The saying is: Be Earnest And (right here at the 3rd flat, you "stop and drop". So Bb Eb and Ab, you simply go back to the previous flat for the proper key signature.
1 flat = F; 2 flats is Bb; 3 flats is Eb; 4 flats is Ab; 5 flats is Db; 6 flats is Gb and 7 flats is Cb. Also notice how they climb by fourths. F to Bb is a fourth; Bb to Eb is a fourth and so on. Sharps climb by fifths.