If I have gambling winnings of $5K and I am not able to itemize since standard deduction is higher, can I reduce my taxable income any other way? Contribute to 401K?

Your gambling winnings is income which you can use as you wish.  Maximizing contributions to a retirement plan is always a good idea but whether you get a tax credit for doing so depends on many factors such as AGI, retirement distributions and other factors. 

Thanks. But considering all other factorss remain unchanged except:

- Addition of $5K to income (W2G)

- Extra contribution of $5K towards 401K or IRA

Will that considered to be a wash?

Yes ... one will offset the other.