You should consider installing IE 6.0 SP1 as soon as possible
Internet Explorer 6 Service Pack 1 (SP1) is the most recent version of the Internet Explorer 6 core technologies in Windows XP Home Edition and Windows XP Professional. Internet Explorer 6 Service Pack 1 provides a reliable and flexible browsing experience and the freedom to experience the best of the Internet for users of Windows XP, Windows Millennium Edition (Windows Me), Windows 2000, Windows 98, and Windows NT 4.0 Service Pack 6a. Total download size for a typical installation is approximately 25 megabytes (MB). However, because setup downloads only those files that are necessary for your computer, this size can vary between 11 and 75 MB.
If you still need IE 5.01 make sure you have SP2
First, if you're not using them by now, make sure you download and install SP2 for IE 5.01. Read more about SP2:
Note: Microsoft has stopped supporting Internet Explorer 5.5 SP2. To download IE5.5 SP2 you'll need to find a different link (with Google for example). I found one for you but I don't know how long it will last because it is an outside link that is NOT controlled by me. Try it and if you find that it stopped working please let me know.
See the Download Other IE Versions page for other IE versions.
As for downloading the entire IE installation files to your local computer for future use - read the Download the full IE package page.
Internet Explorer 5.01 SP2, 5.5 SP2 and IE 6.0 require the following security-related patches:
This update replaces the update that is included with Microsoft Security Bulletin MS05-038. That update is also a cumulative update.
This update does include Hotfixes that have been released since the release of MS04-004 or MS04-025, but they will only be installed on systems that need them. Customers who have received Hotfixes from Microsoft or from their support providers since the release of MS04-004 or MS04-025 should review the “I have received a Hotfix from Microsoft or my support provider since the release of MS04-004. Is that Hotfix included in this security update?” question in the FAQ section of this bulletin to determine how you can make sure that the necessary Hotfixes are installed. Microsoft Knowledge Base Article 896688 also documents this in more detail.