How to set format of std::scientific

I want to print 12345.0 as 0.12345e+05. But the below code gives 1.23450e+04. Is there a way to control the format of std::scientific?

#include <iostream>
#include <string>
#include <sstream>

using namespace std;


int main()
{
    double a = 12345.0;

    std::stringstream s;

    s.precision(5);

    s << scientific;

    s << a;

    cout << s.str() << endl;

    return 0;
}

The output is

1.23450e+04