Trying to interpret figured basses “in the wild” by the rules that you learned to do harmony exercises in music theory exams often doesn’t work!
My pragmatic view (based more on looking at old scores than reading modern texts describing what the notation is supposed to mean) is that a slashed figure tends to mean “a semitone higher, unless that’s obviously stupid, in which case it means a semitone lower”.
The particular example is further complicated because the note with the figures has an accidental itself. Whether the figuring is supposed to be related to the original key signature, or just to the bass note, is another “non-standard, use your common sense” issue. (Some baroque recitatives are harmonically adventurous enough that they stretch the concept of “being in a key” to breaking point in any case).
Assuming that slashed 5 must mean something, otherwise it wouldn’t be there at all: a 5 without a slash would mean a chord in root position (and would be unnecessary anyway) so it must mean something different from A# C# E#. An augmented chord A# C# Ex doesn’t make any harmonic sense here, so it must mean A# C# E natural.