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1 solution
h(x)=f^2(x)+g^2(x) =>h'(x)=2f(x)f'(x)+2g(x)g'(x) =>h'(x)=2f(x)f'(x)+2f'(x)(-f(x)) =>h'(x)=0 =>h(x)=c and since h(0)=5, so c=5 and hence h(10)=5.