I would first write the node equations. You know the following:
1) For an input of -5V, the voltage at the ADC input should be 0V
2) For an input of +3.3V the ADC input should be 3.3V
3) the network provides an attenuation of 3.3/8.3
4) the network provides an offset of +5V
Here is another hint. When your sensor output -5V your ADC should read Zero. Since you have R2(pin1) at +5Vdc and and R2(pin2) at Zero when the ADC read Zero, this imply that you have the same voltage drop between R2 and (R1+470), so, this tells you right away that R1 = R2-470. Now you can find another equation that will bring a gain has described by the attenuation (3.3/8.3) and you have the two necessary equations to calculate your two unknowned R1 and R2.