how can I install Microsoft SQL Server 2005 Express Edition on Windows 8.1 I can't install Microsoft SQL Server 2005 Express Edition on Windows 8.1.
As per Microsoft Official document 

SQL Server 2005 (the release version and service packs) and earlier versions of SQL Server are not supported on Windows Server 2012 R2, Windows Server 2012, Windows 8.1, or Windows 8. You will receive a warning in the Action Center if Windows 8.1 or Windows 8 detects an instance of SQL Server 2005.

To resolve this issue, upgrade or remove the existing instance of SQL Server 2005.

Please read below link

http://support.microsoft.com/kb/2681562/en-gb

EDIT:

Click on run the program without getting help. It will proceed. Although installation is not supported it would not block you from installing but you are doing it at your own risk. If you want a supported scenario. You can create a VM on windows 8 machine and can install windows server 2003 SP2 on it and then install SQL Server 2005 with SP4 to run supported scenario.