safari 5.1.10 is very slow on imac

Try another browser as a test.

Firefox

See if any of the following questions apply to your computer:

1) Are you running any anti-virus/internet security applications?

2) Are you running any "cleaning/tune-up/optimizations" applications?

3) Any peer-to-peer or torrent downloading software?

4) Any third-party disk backup software that came bundled with an external hard drive?

5) Any online backup scheme other than iCloud (Carbonite; GoogleDrive; MS One Drive)?

6) Did your financial institution ask you to install Trusteer EndPoint Protection (also known as Trusteer Rapport)?

Any one of them can slow your computer. Numbers 1, 2, 3, and 6 can affect Safari performance specifically.