350:5•8-80-5•8+35

Let's solve the expression step by step:

1. Start with the expression: \( 350 : 5 \cdot 8 - 80 - 5 \cdot 8 + 35 \)

2. Perform the division: \[ 350 : 5 = 70 \]

3. Now substitute that back into the expression: \[ 70 \cdot 8 - 80 - 5 \cdot 8 + 35 \]

4. Perform the multiplications: \[ 70 \cdot 8 = 560 \] \[ 5 \cdot 8 = 40 \]

5. Substitute these values back into the expression: \[ 560 - 80 - 40 + 35 \]

6. Now perform the operations from left to right:

   • First, \( 560 - 80 = 480 \)
   • Then, \( 480 - 40 = 440 \)
   • Finally, \( 440 + 35 = 475 \)

So, the final answer is: \[ \boxed{475} \]