If we are looking for the Pythagoras triple that goes with 5 and 7
Check
If the pythagoras is 7, then the third number would be
[tex]\begin{gathered} a^2+5^2=7^2 \\ a^2+25=49 \\ a^2=49-25 \\ a^2=24 \\ a=\sqrt[]{24} \end{gathered}[/tex]If the third number is the hypothenuse, then third number would be
[tex]\begin{gathered} a^2=5^2+7^2 \\ a^2=25+49 \\ a^2=74 \\ a=\sqrt[]{74} \end{gathered}[/tex]Please note that square root of 24 and the square root of 74 would not give a whole number.
Hence their is no whole number that goes with 5 and 7 to make a pythagoras triple