What Mac do you have, and what year was it made?
The version of Safari used with OS 10.5.8 is just getting too old to display many current web pages. There's no solution except to use a newer version of Safari, and that may require a newer Mac.
I'd suggest you try a different browser, such as:
Firefox (extended version)
iCab.
These may still be able to work with 10.5.8 and load the web pages in question.