On the fifth power

15=125=3235=24345=1024\begin{aligned} {\color{#D61F06}1}^5 &= {\color{#D61F06}1} \\ {\color{#D61F06}2}^5 &= 3{\color{#D61F06}2} \\ {\color{#D61F06}3}^5 &= 24{\color{#D61F06}3} \\ {\color{#D61F06}4}^5 &= 102{\color{#D61F06}4} \\ \end{aligned}

Is it true that the last digit of a whole number and that of its fifth power are always the same (in base 10)?

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