If the open string is the first note in the scale, the fifth is the note played by the fourth finger, which is the same note as the next open string up. A perfect fifth is where the ratio of the frequency of the sound waves of the notes is 3:2, and is something you can learn to hear. To hear what the fifth sounds like, play first the A string, then immediately play the E. If you are skilled enough, play both at once.
Inexpensive electric tuners do not have the precision to tune a violin to the exact 3:2 ratio, so players who need that much precision learn to tune by ear. If you've only recently learned to tell the difference between sharps and flats, you may not yet be skilled enough at listening to do that yet. Get a teacher or an very good player to show you what it sounds like. If you can't tell the difference between close and perfect yet, don't worry about it, and keep tuning to the tuner. Listening is just as much of a skill as playing. Tuning by ear took me about a year to learn to do as well as a cheap tuner, and I still can't beat a high quality tuner.
If you are a beginner, just tune to the electronic tuner. It is definitely close enough for everyday use, especially once you learn to hear what a fifth on the violin should sound like and can finish off your tuning by ear.
The problem with checking your tuning by playing a fingered note is that it is impossible to place your finger precisely enough. You can tune the instrument with the most precise tuner in the world, and it won't solve the problem of misplaced fingers. When things sound off when you play the open E + the fourth finger on the A string, then your finger is probably off by some fraction of a millimeter (or more). What makes it so noticeable is that you are playing the same note on two strings, so any tiny discrepancy is obvious. This is why tuning is always done to open strings on the violin.