350:5•8-80-5•8+35

To solve the expression \( 350:5\cdot8-80-5\cdot8+35 \), we will follow the order of operations (PEMDAS/BODMAS).

1. First, we perform the division and multiplications from left to right.

   \( 350:5 = 70 \)

   So we replace it:

   \( 70\cdot8 - 80 - 5\cdot8 + 35 \)

2. Now, perform the multiplications:

   \( 70\cdot8 = 560 \)

   and

   \( 5\cdot8 = 40 \)

   Now, replacing these gives us:

   \( 560 - 80 - 40 + 35 \)

3. Now, we will perform the additions and subtractions from left to right:

   First, \( 560 - 80 = 480 \)

   Then, \( 480 - 40 = 440 \)

   Finally, \( 440 + 35 = 475 \)

So, the final result is:

\[ \boxed{475} \]