to a solution you have added hydrogen ions to reduce the pH by 1. By how much has the concentration of hydrogen ions been changed?

Let pHₒ be the original pH, and [H⁺]ₒ be the original concentration of hydrogen ions.
pHₒ = log[H⁺]ₒ ...... [1]

When pH = pHₒ + 1 :
pHₒ + 1 = log[H⁺] ...... [2]

[2] - [1] :
1 = log[H⁺] - log[H⁺]ₒ
1 = log([H⁺]/[H⁺]ₒ)
log(10) = log([H⁺]/[H⁺]ₒ)

Then, [H⁺]/[H⁺]ₒ = 10
or [H⁺] = 10[H⁺]ₒ

The concentration of hydrogen ions is changed to 10 TIMES of the original concentration.

The concentration of hydrogen ions has been increased by a factor of 10.

The [H+] has increased 10 fold.
If the initial [H+] = 5*10^-5M - pH = -log(5*10^-5) = 4.30
If you increase [H+] 10 fold , [H+] = 5*10^-4M - pH = -log (5*10^-4) = 3.30

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