how can i add more memory to 10.5.8

There are two kind of 'memory' that may relevant here. RAM (random access memory) is the working memory in your system, used for active applications/data, and is usually measured in gigabytes (GB) - such as 4GB, 8GB, 16GB, etc.

Then there's persistent storage 'memory', or disk space which is generally data at rest (e.g. all your applications, documents, configurations, preferences, etc.) and almost always exceeds the RAM on your computer (the system can store a lot more data than it can (or needs to) actively process). Typically storage memory is measured in hundreds of GB (e.g. 256GB, 512GB) or terabytes (1TB, 4TB, etc.)

Insufficient amounts of either of them can impact performance, so it's important to know which one you're running out of.

Moving data to 'the cloud' might be a solution if you're running out of disk space - you could add additional disks of provide more space, or move some data to the cloud, thereby freeing up some space on your local disk, but it won't make any difference to the RAM in your system. If it's RAM you're running out of, your only options are to do less (e.g. run fewer applications at once), or upgrade the RAM to give you more headroom.

So, do you know which 'memory' you need more of?