[Valmont]

See if you like this sort of a setup. There are a few minor things to improve, there is a lot to play with:

#include <iostream>
#include <fstream>
#include <string>

using namespace std;

void get_student_grades(ifstream&, int*);
int calc_total_score(const int*, const int);
char calc_grade(int avg);
void save_record(ofstream& file, string name,int* arr, int size, int avg);

int main ()
{
  string StudentName;
  //Always initialize arrays when possible: prevents weird behaviour. int Grades[5] = {0};
  int TotalScore(0);
  int AverageScore(0);
  //--
  
  ifstream StudentDB("students.txt");
  //Could the file be opened without any errors? if(!StudentDB)
  {
    cout<<"Couldn't open file (correctly). Exiting application..."<<endl;
    return(1);
  }
  //Let's create a file to store formatted data.
  ofstream FmtDB("grades.txt");
  //Setup the header of the formatted data on a different file.
  FmtDB << "Name\tScore 1\tScore 2\tScore 3\tScore 4\tScore 5\tAverage\tFinal\t"<<endl;
  //-- while(StudentDB >> StudentName)
  {
    //First, let's collect data.
    get_student_grades(StudentDB, Grades);
    TotalScore = calc_total_score(Grades, 5);
    AverageScore = TotalScore/5;
    //Second, we store the record on already prepared file.
    save_record(FmtDB, StudentName, Grades, 5, AverageScore);
  }
  //-- return 0;
}

//------------------------------------- void get_student_grades(ifstream& dbase, int* arr)
{
  unsigned i(0);
  while(dbase >> arr[i])
  {
    ++i;
  }
  //Give database file back in a decent state.
  dbase.clear();
}

//------------------------------------- int calc_total_score(const int* arr, const int size)
{
  int total(0);
  for(int i = 0; i < size; ++i)
  {
    total += arr[i];
  }
  return total;
}

//------------------------------------- char calc_grade(int avg)
{
  if (avg >= 90)
    return 'A';
  if (avg >= 80)
    return 'B';
  if (avg >= 70)
    return 'C';
  if (avg >= 60)
    return 'D';

  //Bad student: score lower then 60. return 'F';
}

//------------------------------------- void save_record(ofstream& file, string name, int* arr, int size, int avg)
{
  file << name <<"\t";
  for(int i = 0; i < size; ++i)
  {
    file << arr[i] << "\t";
  }
  file << avg << "\t";
  file << calc_grade(avg) <<endl;
}