I have Takamine EG540SC like the one in this picture:

The action on the Low E String is about 5mm above the 12th fret. Is that a little too high?
5mm is actually a decent height there. If your comfortable with changing it, you could remove the saddle and sand to bottom surface of it to lower the action a tad. Be warned tho, if you remove too much, you can't put it back! A little goes a long way in other words. As long as it doesn't buzz anywhere along the neck, go for it.
If you do decide to sand the saddle, make sure to tape a large piece of 250 grit sandpaper down to a totally flat surface, then work the saddle on that. It gives you more control and insures a flat bottom on the saddle as you go. Btw, this little procedure will also lower all of the other strings as well. You have been warned.
Nice axe too. And a lefty to boot!
Only if you don't like it that high, the idea is to change the action to a place that suits you. If you like it where it is and it is comfy and easy for you to play, and you like the sound, leave it there.
well if you like it that high its fine if you dont then its not. mines like 4mm above 12th and its a bit high, but if you like it liek that its fine.
I'll believe in anything and you'll believe in anything.