1

This is the version of the question WHICH DOESN’T USE KEY SIGNATURES.  Each note has to be worked out or checked by writing it up or down the stated  interval, in this case up a perfect 5th.

2

The first step is easy. Just write out each note-head a 5th  higher - i.e. two lines above (if a line note) or two spaces above ( if  a space note). Leave a space before each note-head to add accidentals in step 2

Note by note, check whether an accidental is needed and if so write it in.  

First note:  Perfect 5th above G# is D#  - # needed

Second note: Perfect 5th above  B is F#  - # needed etc

The transposition of a 5th up from a B ond Bb are classic cases where an accidental is needed in the transposition but not in the original (B - F#) or vice versa ( Bb - F). The natural sign against the F quaver in bar 3 is not strictly needed - it’s well to add this cautionary accidental though, given the F# sharp in the previous bar, to show that you have considered this note. In practice, such chromatic music as this would have cautionary accidentals added.