Elementalist is suffering from a mana problem

It's a normal item (not corrupted)?

You can change the socket color and roll it with alchemy/essence.

And if you're worried about not having enough chromatic orbs to get the colors you want, check out the Vorici Calculator: http://siveran.github.io/calc.html

Green is no problem, if you got beacon of ruin in your ascendancy, like you should. Get some flat cold damage added to spells somewhere (easiest slot is usually a hypnotic eye abyss jewel). The amount doesn't matter. Boom - you can use hypothermia. (This only works with Elementalist - Beacon of ruin.)

Two red is kinda rough though. The only decent red dps support for Arc is Empower afaik, and that might be a tad expensive to obtain for a newbie.

You could recoulour your chest and try to get not more than one red and/ or one green socket. Any number of blue is fine, there are tons of good blue supports for Arc.

6 blue, 5 blue, one red or one green and four blue one red one green all work fine. To get one of these results shouldn't be too difficult.

I managed to roll six blue sockets on my Chainmail. Not sure how I got lucky with that but now I have them I don't want to risk changing them again :)

I used an essence on it and got life on it ...

I am still taking some big hits when mapping though ...

you can still use the master benches to craft onto your armor and shield.

your ruby ring is just awful. it has 25 light+fire resist, and nothing else useful. the mana leech is PHYSICAL damage leeched as mana, but you dont deal physical damage.

so, swap that ring for something with Life, and make sure to use those open craft slots.

Don't use elemental prolifewration support. You already get the same effect from your ascendancy. Use innervate, faster casting, arcane surge or efficacy support. My personal choice would be faster casting, but they all make some sense.