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Order of Operations are:
* Parentheses (Brackets) first
* Exponents (Orders, Powers, Square Roots, etc.) next
* Multiplication and Division (left-to-right) next
* Addition and Subtraction (left-to-right) last

So we do the Division and Multiplication before the Addition and Subtraction:
So 5 × 4 = 20
2 × 3 = 6
and 16 ÷ 4 = 4
Therefore
5 × 4 - 2 × 3 + 16 ÷ 4
= 20 - 6 + 4

Subtraction and Addition  rank equally, so we do the Subtraction next and then the Addition
Therefore
20 - 6 + 4 = 14 + 4 = 18

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30 - (5 × 2³ - 15) =
30 - (5 × 8 - 15)

[Remember that 2³ means 2 × 2 × 2 = 8, not 2 × 3 = 6]

Next Multiply:
30 - (5 × 8 - 15) = 30 - (40 - 15)

Next Subtract:
30 - (40 - 15) = 30 - 25

Now the Brackets are completed, the last operation is Subtract:
30 - 25 = 5


IN SHORT:
30-(5×2³-15)
=30-(5×8-15)
=30-(40-15)
=30-25
=5

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Start with: (3 + 2)² - 5 × 3 + 2³
Do the Bracket first: (3 + 2) = 5
⇒ 5² - 5 × 3 + 2³
Next we do the Orders: 5² = 25 and 2³ = 8
⇒ 25 - 5 × 3 + 8
Next we do the Multiplication:
⇒ 25 - 15 + 8
Finally we do the Addition and Subtraction, in left-to-right order:
⇒ 10 + 8
⇒ 18

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First Bracket:
4² - 6 + 5
Do Order first:
4² - 6 + 5 = 16 - 6 + 5
Then do Subtraction and finallyAddition:
16 - 6 + 5 = 10 + 5 = 15

Second Bracket:
3² + 8 - 7 × 2
Do Orders first:
3² + 8 - 7 × 2 = 9 + 8 - 7 × 2
Next do Multiplication:
9 + 8 - 7 × 2 = 9 + 8 - 14
Next do Addition and finally Subtraction:
9 + 8 - 14 = 17 - 14 = 3

Now we've simplified what's inside the two sets of Brackets, we can complete the problem with the final Division:
(4² - 6 + 5) / (3² + 8 - 7 × 2) = 15 / 3 = 5

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So we should work out what's inside the Brackets first. There are two sets of Brackets, so do one at a time.

First Bracket:
7 - √9
Do Order (in this case square root) first:
7 - √9 = 7 - 3
Then do Subtraction:
7 - 3 = 4

Second Bracket:
4² - 3 + 1
Do Orders (the squaring) first:
4² - 3 + 1 = 16 - 3 + 1
Next do Subtraction:
16 - 3 + 1 = 13 + 1
Next do  Addition:
13 + 1 = 14

Now we've simplified what's inside the two sets of Brackets, we can complete the problem with the final Multiplication:
(7 - √9) × (4² - 3 + 1) = 4 × 14 = 56