After knowing a bit about this image library and analyzing the question graph, I can comment on some possible causes of slowness ...
TimThumb is always processing all images
This does not seem to be the case, as several lines of the graphs show only green bars, which means that time was spent with image transfer rather than processing.
Note that it does not make much difference for the URL to be tim.php
, as long as the library is just writing a cache image to the output as this is quick.
In any case, make sure that the images are being written to the directory set to cache. If they are not, adjust the script's permission for the folder.
TimThumb is sending some header which prevents caching
Use your browser's browser developer tool ( F12 ?) to monitor the network and verify that after accessing the same page a second time, images will be uploaded of the browser cache and not download again.
Your server is slow
Honestly, for some shared hosting, 5 seconds is up to a reasonable time for the level of processing your site seems to be using. I even use bluehost for my blog, and if it were not for the Wordpress cache plugins, the loading time could easily double that.
Large number of downloaded files
Another factor seen in the chart is that there are a large number of elements downloaded in the page access. This also has a negative impact, even if your network bandwidth is good, because browsers limit the number of simultaneous connections. The limit is usually between 2 and 6 connections ( see this answer from SOEN ).
However, this would be greatly mitigated in your case after the second access to the site, because at least web fonts , styles and scripts would be cached in the browser. Of course the price would be paid on the first access, but if the content is good it's worth it.
Conclusion
I'm inclined to think that there is not a specific problem with TimThumb.
I would do some testing by placing static images and also checking if the browser is able to use the cache properly and load the page more quickly from the second access.
Finally, if the question were performance, there are techniques to improve this, such as hiring a more powerful server or even more specialized cloud caching services.