Hi Carole
Answer to your question is "yes".
Have a look at
this Apple article for installing other software, including Safari, from the Tiger DVD - see the section titled More custom reinstallation options with Mac OS X 10.4.
Other Steps
Move the Safari.pkg file in the HD>Library>Receipts folder to the trash.
As a precaution, prior to reinstalling Safari, move your
Safari folder, found via the Finder in your Home Folder>Library to the Desktop. It has your bookmarks, history etc. Once the reinstall is completed, move the folder back to its original location writing over the newly created folder.
Remember too, the version of Safari you install will be specific to the Version on your installer DVD. Therefore, run Software Update and see if Safari updates appear. (Your post tag says 10.4.5. I suspect you are using 10.4.10, which is the latest version of OS X Tiger. If not, please let me know, disregarding the following comment.) If not, reapply the 10.4.10
combined update to bring Safari up to the current version.
"Repair Permissions" via Disk Utility in your Utilities folder when you are finished.