Certainly! Let's solve each equation for \( x \).

1) \( (x + 5)^2 + 16 = 80 \)

\[
(x + 5)^2 = 64
\]

\[
x + 5 = \pm 8
\]

\[
x = 3 \quad \text{or} \quad x = -13
\]

2) \( (x + 2)^3 - 23 = 41 \)

\[
(x + 2)^3 = 64
\]

\[
x + 2 = 4
\]

\[
x = 2
\]

3) \( 37 - (x - 2)^2 = 28 \)

\[
(x - 2)^2 = 9
\]

\[
x - 2 = \pm 3
\]

\[
x = 5 \quad \text{or} \quad x = -1
\]

4) \( (3x - 15)^2 - 6 = 75 \)

\[
(3x - 15)^2 = 81
\]

\[
3x - 15 = \pm 9
\]

\[
3x = 24 \quad \text{or} \quad 3x = 6
\]

\[
x = 8 \quad \text{or} \quad x = 2
\]

5) \( 100 + (3x - 1)^3 = 108 \)

\[
(3x - 1)^3 = 8
\]

\[
3x - 1 = 2
\]

\[
3x = 3
\]

\[
x = 1
\]

6) \( (3x - 4)^3 = 7 + 1^{2019} \)

\[
(3x - 4)^3 = 8
\]

\[
3x - 4 = 2
\]

\[
3x = 6
\]

\[
x = 2
\]

7) \( (2x - 5)^3 = 15^2 - 4.5^2 \)

Let's calculate the right side:

\[
15^2 = 225
\]
\[
4.5^2 = 20.25
\]
\[
225 - 20.25 = 204.75
\]

Then solve \( (2x - 5)^3 = 204.75 \) (this indicates \( x \) is not an integer, exact solution would require solving this cubic equation numerically).

8) \( (x + 2)^7 = 5^5.5^2 \)

Calculate the right side:

\[
5^5 = 3125
\]
\[
5^2 = 25
\]
\[
3125 \times 25 = 78125
\]

Then solve \( (x + 2)^7 = 78125 \).

9) \( (3x - 6)^3 = 81 \)

\[
3x - 6 = 3
\]

\[
3x = 9
\]

\[
x = 3
\]

10) \( 81:(7x - 11)^3 = 3 \)

\[
(7x - 11)^3 = 27
\]

\[
7x - 11 = 3
\]

\[
7x = 14
\]

\[
x = 2
\]

11) \( (2x + 1)^3 = 108:4 \)

\[
(2x + 1)^3 = 27
\]

\[
2x + 1 = 3
\]

\[
2x = 2
\]

\[
x = 1
\]

12) \( (2x - 3)^2 = 1 + 5.4^2 \)

Calculate the right side:

\[
5.4^2 = 29.16
\]
\[
1 + 29.16 = 30.16
\]

Then solve \( (2x - 3)^2 = 30.16 \).

13) \( (3x - 2)^3 - 14 = 2.5^2 \)

Calculate the right side:

\[
2.5^2 = 6.25
\]
\[
(3x - 2)^3 = 20.25
\]

Then solve \( (3x - 2)^3 = 20.25 \).

14) \( (3x - 4)^3 = 5^2 + 4.5^2 \)

Calculate the right side:

\[
5^2 = 25
\]
\[
4.5^2 = 20.25
\]
\[
25 + 20.25 = 45.25
\]

Then solve \( (3x - 4)^3 = 45.25 \).

15) \( (3x + 4)^2 = 3^2 + 2^3 + 83 \)

Calculate the right side:

\[
3^2 = 9
\]
\[
2^3 = 8
\]
\[
9 + 8 + 83 = 100
\]

Solve \( (3x + 4)^2 = 100 \).

16) \( (7x - 11)^3 = 2^5.5^2 + 200 \)

Calculate the right side:

\[
2^5 = 32
\]
\[
5^2 = 25
\]
\[
32 \times 25 = 800
\]
\[
800 + 200 = 1000
\]

Then solve \( (7x - 11)^3 = 1000 \).

For some equations, numerical methods or calculators might be required for non-integer solutions.