FindRoot does not work II

Questions
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3

This is the exact same issue as in the previous post (in V9 and later Integrate returns a ConditionalExpression).
Try

ClearAll["Global`*"]
f[x_] = x^2;
s[x_] = Integrate[Sqrt[1 + (f'[t])^2], {t, 0, x}, Assumptions -> x > 0];
FindRoot[s[x] == 5, {x, 2}]

Another way:

ClearAll["Global`*"]
f[x_] = x^2;
s[x_] = Integrate[Sqrt[1 + (f'[t])^2], {t, 0, x}];
FindRoot[Normal[s[x]] == 5, {x, 2}]

And a third way, using _?NumericQ

ClearAll["Global`*"]
f[x_] = x^2;
s[x_?NumericQ] = Integrate[Sqrt[1 + (f'[t])^2], {t, 0, x}];
FindRoot[s[x] == 5, {x, 2}]