2010 535i Sports Mode/Paddle shifters questions

Hi, I'm a Newbie to this forum and owning a Bimmer...

I have a 2010 535i with Sports/Premium package. But I don't see any sports mode button in the interior, Am I missing something ? I notice the suspension and steering feels a little sturdy but I was under the assumption I could engage the sports mode by Pressing a button.

I did notice the DS mode on the shifter but is that it ?

Also my car doesn't come with factory installed PADDLE shifters even though it claims to be a SPORTS PACKAGE. Is it possible to have it installed right now via after market parts ?

Thanks and really looking forward for people to educate me further.

This forum is amazing and I'm learning new things everyday.

Model-specific questions are best answered in the forum for that model, in your case one of the 5 Series forums. You're more likely to get help from other people that own the same model that you do. This forum is for General BMW discussion, not model-specific discussion.