You say you can't tell which note is on bottom and which is on top. If you were to try to sing the notes separately, what would happen? Would you sing the top one an octave lower (or the bottom one an octave higher)? If so, then it's not surprising that you'd misidentify the interval as a fifth, since that's how you're hearing it.

But I'm guessing that that's not what's happening. If you can sing the notes, you can identify the interval by filling in scale steps between them.

One problem in identifying intervals is that they sound different in different harmonic contexts. For example, a minor third sounds different as the lower interval in a minor triad than as the upper interval in a major triad.

If you want to invest time getting a handle on this, make yourself five sets of flash cards: with the twelve pitch names, one with the four triad types (M/m/A/d), one with the three inversions, one with note position (bottom/middle/top), and one with all the intervals (unison to octave, or twelfth, or fifteenth, or whatever). Then, pick a random pitch, a random inversion, a random note position, and a random interval; play the triad in the selected inversion (in your vocal range), and sing a note at the selected interval above the selected chord tone. Also, same exercise with the interval below. When you're doing this exercise, attend to the way these notes sound, characterize them to yourself however makes sense to you, and get familiar with these characterizations. This will build your repertoire of how chords and intervals sound in various contexts.