Simplify the given expression:

3(7+x) + 5 + 2(y+z) - 2x - 1 + 3z
= 21 + 3x + 5 + 2y + 2z - 2x - 1 + 3z
= 17 + x + 2y + 5z

Therefore, the simplified expression is 17 + x + 2y + 5z.