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I would create a class and define an input operator:

struct Person
{
    std::string name;
    std::string age;
    std::string salary;
    std::string hoursWorked;
    std::string randomText;

    friend std::istream& operator>>(std::istream& str, Person& data)
    {
        std::string line;
        Person tmp;
        if (std::getline(str,line))
        {
            std::stringstream iss(line);
            if ( std::getline(iss, tmp.name, ':')        && 
                 std::getline(iss, tmp.age, '-')         &&
                 std::getline(iss, tmp.salary, ',')      &&
                 std::getline(iss, tmp.hoursWorked, '[') &&
                 std::getline(iss, tmp.randomText, ']'))
             {
                 /* OK: All read operations worked */
                 data.swap(tmp);  // C++03 as this answer was written a long time ago.
             }
             else
             {
                 // One operation failed.
                 // So set the state on the main stream
                 // to indicate failure.
                 str.setstate(std::ios::failbit);
             }
        }
        return str;
    }
    void swap(Person& other) throws() // C++03 as this answer was written a long time ago.
    {
        swap(name,        other.name);
        swap(age,         other.age);
        swap(salary,      other.salary);
        swap(hoursWorked, other.hoursWorked);
        swap(randomText,  other.randomText)
    }
};

Now your code looks like this:

Person   data;
while(readFile >> data)
{
    // Do Stuff
}

PS. I noticed you were using string and ifstream without the std::. This suggests you have using namespace std; in your code. Please don't do that. see Why is “using namespace std;” considered bad practice?

Don't explictly close() a file unless you are going to check that it worked (or are going the re-open). Prefer to let the destructor do the closing (that way it is exception safe). See: My C++ code involving an fstream failed review