I can't even turn my Iphone 5s on?

I can't even turn my Iphone 5s on? - 1

If there's water damage some likely short circuited. Or the battery could just be old and need to be replaced. Also if it turns on but you don't see anything, the screen is the issue

Go to your network provider whether that is EE 3 Vodafone and see what your options are and if you can get it fixed based on the contract your on.

Get a competent repair shop to diagnose the cause of the fault and estimate the repair costs and then decide whether to go ahead or replace your old phone.

Competent repairers will usually have to charge for the diagnostic work but then usually come up with an honest appraisal and a realistic (though not guaranteed) repair estimate. Many other repair shops will offer a free opinion which is rarely any more than a guess and will then often present you with a higher than expected bill for the repair.

Try to see if it powers up when you connect it using the Lightning cable to iTunes on a host computer. If it does, carry out a full back up and select the option to back up apps as well (takes longer). If the phone does power up on iTunes then there's a fair chance that it's just got a faulty power button or a completely failed battery. If it doesn't power up then it's likely not worth repairing but if it's in good cosmetic condition will still have a resale value for "spares or repairs".

Its got a broken lock button o rneeds a new battery