What is the Rth on the circuit
I think the offset should be 2.0625V, not 3.3/2 + 1 (2.65V).

Using @Tony Stewart Sunnyskyguy EE75 offset calcuated at Vin = -5 and 3V:
\$Vout=Gain*Vin + Offset\$
\$Vout= \dfrac{3.3}{8} * Vin + \dfrac{3.3}{2}+1 \$
\$Vout(Vin=-5V) = \dfrac{3.3}{8} * (-5) + \dfrac{3.3}{2}+1 = 0.5875V\$
\$Vout(Vin=3V) = \dfrac{3.3}{8} * (3) + \dfrac{3.3}{2}+1 = 3.8875V\$

Both of these endpoints are incorrect by a constant value of 0.5875V. This suggests that the gain is correct and the offset value is incorrect.
Because the gain is multiplying the input, the average value of the input also changes.
\$Avg(Vin) = -1\$
\$Avg(Vin*Gain) = -\dfrac{3.3}{8}\$

Calculating the offset needed to bring up the scaled signal midpoint to 1.65V:
\$Offset = \dfrac{3.3}{2} - \dfrac{3.3}{8} * \dfrac{-5 + 3}{2}\$
\$Offset = 2.0625V\$

Checking this with the Vin endpoints again (and Vin midpoint),
\$Vout=Gain*Vin + Offset\$
\$Vout= \dfrac{3.3}{8} * Vin + 2.0625 \$
\$Vout(Vin=-5V) = \dfrac{3.3}{8} * (-5) + 2.0625 = 0.0V\$
\$Vout(Vin=-1V) = \dfrac{3.3}{8} * (-1) + 2.0625 = 1.65V\$
\$Vout(Vin=3V) = \dfrac{3.3}{8} * (3) + 2.0625 = 3.3V\$