Is it possible to style html5 audio tag?

Yes! The HTML5 audio tag with the "controls" attribute uses the browser's default player. You can customize it to your liking by not using the browser controls, but rolling your own controls and talking to the audio API via javascript.

Luckily, other people have already done this. My favorite player right now is jPlayer, it is very stylable and works great. Check it out.

Yes: you can hide the built-in browser UI (by removing the controls attribute from audio) and instead build your own interface and control the playback using Javascript (source):

<audio id="player" src="vincent.mp3"></audio>
<div> 
  <button onclick="document.getElementById('player').play()">Play</button> 
  <button onclick="document.getElementById('player').pause()">Pause</button> 
  <button onclick="document.getElementById('player').volume += 0.1">Vol +</button> 
  <button onclick="document.getElementById('player').volume -= 0.1">Vol -</button> 
</div>

You can then style the elements however you wish using CSS.

MDN HTMLAudioElement API reference

<audio>

audio::-webkit-media-controls-panel

audio::-webkit-media-controls-mute-button

audio::-webkit-media-controls-play-button

audio::-webkit-media-controls-timeline-container

audio::-webkit-media-controls-current-time-display

audio::-webkit-media-controls-time-remaining-display

audio::-webkit-media-controls-timeline

audio::-webkit-media-controls-volume-slider-container

audio::-webkit-media-controls-volume-slider

audio::-webkit-media-controls-seek-back-button

audio::-webkit-media-controls-seek-forward-button

audio::-webkit-media-controls-fullscreen-button

audio::-webkit-media-controls-rewind-button

audio::-webkit-media-controls-return-to-realtime-button

audio::-webkit-media-controls-toggle-closed-captions-button

REFERENCE: https://chromium.googlesource.com/chromium/blink/+/72fef91ac1ef679207f51def8133b336a6f6588f/Source/core/css/mediaControls.css?autodive=0%2F%2F%2F