So far you have learnt the open strings of the mandolin and all the natural notes in the first five frets plus one sharp (F#) and one flat (Bb). If you want to be a good musician, it is necessary to learn all the notes on the fretboard and also know how to read them. This means learning the sharps and flats which occur in between all of the natural notes.
A semitone is the smallest distance between two notes used in western music. On the mandolin, notes which are a semitone apart are one fret apart (e.g., the note C on the 3rd fret, 2nd string is one semitone above the note B at the second fret). This could also be reversed i.e., the note B is one semitone (one fret) below the note C. Notes which are a tone (two semitones) apart, are two frets apart. An example of this would be the notes A and B on the 4th string. Check this on the following diagram and also on your mandolin.