Is there a way to set the size of the history list in bash to more than 5000 lines?

No matter how much I set the HISTSIZE environment variable to be larger than 5000, when printing the history list with the history builtin, it prints only the last 5000 commands.
I need that because I often have a large .bash_history which exceeds 5000 lines, and sometimes one needs to address an early command by pressing Ctrl-R, but if that command is more than 5000 commands earlier, I can’t access it using that mechanism. I know I can use grep on the .bash_history, but I think the Ctrl-R mechanism would be much more faster (and convenient). I use gnu bash version 4.1.