Occasionally you may come across the figure “5” in a figured bass line. Figured bass numbers were originally intended as chord notation for continuo players, who would improvise a chord-based accompaniment on an instrument such as the harpsichord. With a “blank 5/3”, the continuo player would automatically know to play a root position chord, and it would be up to them to decide exactly how to play it, within the normal rules of harmony. The normal rules for a root position chord require that the root and 3rd of the triad must be included, but that the 5th is optional.
If the 5 is written as a figure, then the 5th is longer optional for the continuo player – the realisation must include a 5th. You need a complete three-note root position triad.
When figured bass is used in harmony questions such as the ABRSM Trio Sonata at Grade 8, the interpretation of “5” becomes less clear, because you are being asked to fill in a melody part by using the figured bass, rather than use it to create a chordal accompaniment. This, of course, is not what the figured bass was originally intended for. It is quite possible that the 5th was only needed in the continuo part, and not in the melody parts.
If you are doing a harmony question, most of the time the best approach is treat the figures literally, so if there is a 5, include a 5th. But sometimes it is just not possible to include a literal realisation of the figures, and in those cases it is best to write a melodically good part (good voice leading within the individual part) and trust that the continuo player would supply the “missing” note.
In this example from Corelli’s Trio Sonata Op.3/2, the figure 5 appears twice. In both cases, it is because the 5th of the triad should not be omitted.
In some cases, the figure 5 is written because the 5th of the triad needs a chromatic alteration. In this example (Corelli Op.1/6), the 5♮ is used because the 5th needs to be naturalised after the preceding A#: