1)
First, rewrite the logarithmic inequality in exponential form:
5^(log5) > 5^2

This simplifies to:
8x + 1 > 25

Now solve for x:
8x > 24
x > 3

Therefore, the solution to the inequality is x > 3.

2)
First, distribute the 1/2 to the terms inside the brackets:
(1/2) 5x - (1/2) 14 < 16
5x/2 - 7 < 16

Now, add 7 to both sides:
5x/2 < 23

Multiplying by 2 to remove the fraction:
5x < 46

Now, divide by 5 to solve for x:
x < 46/5
x < 9.2

Therefore, the solution to the inequality is x < 9.2.