Need value in cell to reflect choice of drop down menu in adjacent cell

I have created a drop down list with 5 different city names for choices. I am trying to get the cell next to it to reflect the outcome of cell on another worksheet based on the city choice. On the other worksheet I have each city with different shipping rates varied by weight. This worksheet will be hidden. I have gotten one of the cities to work properly but I am at a loss on how to get all 5 working. Any ideas? I used this code to get one city working. =IF((A4={"Houston"}),Formulas!C1)

Sounds like the VLOOKUP function in the adjacent cell might be one possible way forward.

Thanks, I was heading on that path but was not sure if it was the correct way to go. My only problem was when looking into the VLookup it appear to me the cells must be on same worksheet.