How do I backup my photos of about 80GB onto my laptop?

Ok so whenever I try to backup my photos of about 80GB on my iPhone 6s of 128GB my laptop just tells me “no device found” (even though I plug it in with the USB cable). And then sometimes my laptop finds the photos and also displays them to me, starts backing up for about 5 seconds and then it says “no device found” again. And I just can’t deal with this any longer! I need to backup my photos immediately (and not to iCloud!). I’m pretty sure its my phone’s fault because whenever I try it with my old Mac it works in the beginning but then it starts stopping and not backing up anymore (but I believe that’s because my Mac is from about 2007). So what should I do? I’m seriously panicking. Also I’ve caught my phone immensely lacking since I don’t have any storage anymore and its just suuuuper slow. I‘m in need for help here. Thanks already.