Kadri Kivistik 

Microsoft hosts new versions of the runtimes on the same URL so the installer is broken.

Install the last version of 2005 runtimes from here https://www.microsoft.com/en-us/download/details.aspx?id=26347 you need the vcredist_x86.exe installer.
Then bypass the setup.exe by double-clicking chainerhost.exe in C:\ProgramData\Package Cache\SDL\SDLTradosStudio2015_SR3

Kadri Kivistik 

Microsoft hosts new versions of the runtimes on the same URL so the installer is broken.

Install the last version of 2005 runtimes from here https://www.microsoft.com/en-us/download/details.aspx?id=26347 you need the vcredist_x86.exe installer.
Then bypass the setup.exe by double-clicking chainerhost.exe in C:\ProgramData\Package Cache\SDL\SDLTradosStudio2015_SR3