Step 1 :Expand the given expression $(3x+5)^2$ using the distributive property: $(3x+5)(3x+5) = 9x^2 + 15x + 15x + 25 = 9x^2 + 30x + 25$
Step 2 :The simplified expression for $(3x+5)^2$ is \(\boxed{9x^2 + 30x + 25}\)