Hey I'm new here but I really need help. I've looked up lots of videos and read into bike repairs but I've hit a bump in the road. Recently recovered a bike from the shed, cleaned it down, bought tools and the extras for it to get it in working condition as my beloved bike was stolen from my garden. Replaced inner tubes, fixed up the brakes which wasn't too difficult... Now, the damn damn damn gears!

I cannot shift from highest into any other gear on the back, and at the front the same. It is a twist shift on the handlebars, and the left one (being the front gear set) is very loose, the twister itself, but will not change gears. Now the problem is almost certainly in the gear cables, they both have much more than 5mm slack despite efforts to tighten them up. This includes trying the cable housing screws and unbolting the cable itself and pulling on it; nothing works, I can't get the slack out of it. I expect I need new cables, but is there anything else I can try before that? When I try to tighten the rear gear cable, it seems that the cable housing is stopping me from getting it any tighter. Also cannot turn the rear cable housing adjustment screw at all, stiff as a rock. Am I not pulling hard enough? Any help is appreciated as I am on low budget but direly want to get out nd ride again.