I think a lot of things can go into playing arpeggios. Usually left hand arpeggios are played in a lower dynamic level than right hand figuration, so playing softer and controlled is important. I would start off by just playing with the 5th finger alone on one note, with the other fingers completely relaxed and resting. Start off slowly and try to just play an even rhythm. Sometimes with the fifth finger even this is tricky at first because it shares a tendon with the 4th and doesn't get as much use as the other fingers. Then try to do that with a range of dynamics, with crescendoes (I wouldn't try to get too loud at first, just bring up the dynamic) and decrescendoes until you have control of the sound in an even tempo, first slowly and then more quickly when you get more comfortable. After you can do those things, I would focus on P and PP dynamics just repeating the note with your fifth finger. Do a little of this every day, to increase both control and fluidity.
As for the arpeggios, one thing you can try, just for practice's sake, is starting with the second note of the arpeggio (if the arpeggio is ascending first). Make sure you can play the whole arpeggio with every finger you use but without the root/5th finger evenly in the desired dynamic. If the arpeggio comes back down, play the note before the fifth finger plays again, and then pause. Give yourself a moment to really focus on the fifth finger, and try playing it in the same dynamic. I'd practice this for a while, and as you get more comfortable, to make less of a gap, until finally there isn't one. I'd pick a phrase (often about four bars) or progression to focus on, so it's a little less repetitive than playing the same arpeggio over and over.
I'm not sure of the type of arpeggio you're playing, but there is often a jump back down to the root where it's hard to not accent with the fifth finger. If this is the case, I'd play the upper notes in tempo, and jump to where the lower note played by the fifth is, with your jump also in tempo, but wait a split second for you to get calibrated and able to focus on the sound you're making. So do the jump but don't immediately try to play--let your hand relax and your mind focus on the sound you want to make, and then play it. Often in jumps we can tense up because we immediately start stretching the fingers in anticipation of the note. This tension can make it harder to control the sound, especially if we're supposed to be playing softly.
If evenness in rhythm or sound is the issue, tension in your fingers and hand (and brain!) can also be contributing to the difficulty. I used to have a lot of tension, and it still crops up in difficult or awkward passages, and something I like to do is to play whatever figure staccato whenever I have tension. When we play legato, we often have to have more than one finger activated at a time. This can especially cause tension in the left hand, because a lot of arpeggios use a fingering like 5421 if they span an entire octave, and 5 and 4 share a tendon. So try playing finger staccato in the desired dynamic, at first slowly and letting your hand and fingers relax between notes. With staccato we start by applying force downward but then let go, letting the rebound of the key push the relaxed finger back up. I often notice that a passage feels so much lighter in my hands when play it staccato a time or few, because it promotes relaxation between notes, when with legato we're activating 2 fingers at once (sometimes more if playing is fast and we're anxious to get the next note in time). Play the note, let go, feel the relaxation coming back into your hand, play the next. Pretty soon you'll be doing this close to tempo, and your hand has learned to do the motions with a lot less tension, so when you come back to a more legato articulation, you can feel the difference. I do this a lot whenever a passage feels heavy or awkward under my fingers, because it's often resistance/tension between fingers in the hands that contributes to this feeling, so if we can practice to minimize that tension we can go back and often play a lot more cleanly and with the kind of articulation we really want.
There's so much that goes into arpeggio playing that you should really talk to your teacher about this. I haven't even touched on rotation and how it can help relieve tension by avoiding "locking" your hand into a stiff position (often when starting out we want to have all of our fingers in place for arpeggios as if we were playing big chords), and sometimes there needs to be a kind of choreography of the hand, especially if there is a mix of black and white keys.
Don't lose hope; these things take time. There's often a steep learning curve and slow, gradual progress, and then one day this will be easy to you.
Topic: Trouble with smooth and even left hand