Once the context is understood, that you are talking about the wires, you don't need to repeat the word "wire" all the time, only when you want to make it clearer. Also if you write in past tense, use past tense for the whole paragraph.
My lamp did not work this morning and I found that the electric cord was broken, so I decided to fix it. I stripped out about 5 cm of the insulation on both broken wires to expose the multi core wires inside. Many of the core wires were stretched out or bent and no longer in their original condition. So I stretched and straightened them using my fingers, then I joined and twisted the core wires together and wrapped the exposed wire with tape, for each of the two wires.