what is the best model to use?

I have been working on this project for over 4 months. My model was approved by supervisor. The model was to run a multinomial logistic regression to see if there is a relationship between 2 categorical variables (both are 1 through 5) while controlling for other variables such as ***, age, socio-economic status, etc. I have ran and reran numerous multiple regression analysis in SPSS and was now told to do it a different way. This is a large database (about 25,000 records). What test should I use? I am trying to see if there is a relationship between two categorical variables and I need to control for things like gender, age etc.

Here’s my thought so far (please comment): I was thinking about using linear regression. Could this work?

What test do you think I should use?

Stats is very difficult for me but I have been working very hard on this. Please help me!