Use a custom function.

Code

function result(range) {
  var splitCol = 1; // split on column B
  var output2 = [];
  for(var i=0, iLen=range.length; i<iLen; i++) {
    var s = range[i][splitCol].split("\n");    
    for(var j=0, jLen=s.length; j<jLen; j++) {
      var output1 = []; 
      for(var k=0, kLen=range[0].length; k<kLen; k++) {
        if(k == splitCol) {
          output1.push(s[j]);
        } else {
          output1.push(range[i][k]);
        }
      }
      output2.push(output1);
    }    
  }
  return output2;
}

Explanation

The script evaluates each row, and particularly the second column of each row (in JavaScript arrays are zero based, so column 2 corresponds to index 1 of the array). It splits the contents of that cell, into multiple values and uses the "\n" as delimiter (line feed). After that it adds the existing info to an array and only add the individual results, when it hits index 1 (k == 1). The newly prepared row is then added to another array, that's being returned to show the result.

Screenshot

data

result

Example

I've created an example file for you: multi-line cells into new rows.

• Add the script under Tools > Script editor.
• Save the script, the name doesn't matter.
• Use the custom function in a cell just like a built in (see the screenshot above).

Short answer

1. Add a new sheet.
2. Add the following formulas to the new sheet

Cell A2 -> Headers

=OFFSET('Form responses 1'!$A$2,ceiling((row()-1)/5,1)-1,0)  

This could be repeated several times, one for each header column, just change the last parameter accordingly.

Cell B2 -> data

=OFFSET('Form responses 1'!$A$2,ceiling((row()-1)/5,1)-1,mod(row()-2,5)*2+1,1,2)

Fill down as necessary

Explanation

• OFFSET() is used to get the values from the source data.
• 'Form responses 1'!$A$2 is the start point to count columns and rows.
• row() is used to increment the row and column iterators.
• ceiling((row()-1)/5,1), row iterator, is used to set the row from the source data.
• mod(row()-2,5)*2+1, column iterator, is used to set the column from the source data.
• In the data formula the last parameter, indicates the number of data columns.

In case that are several "header data" columns, add 1 for each of them. I.E. if there are five "header data" columns, and six "data columns" the column iterator should be

mod(row()-2,5)*6+5

The final data formula to be added to the F2 cell is:

=OFFSET('Form responses 1'!$A$2,ceiling((row()-1)/5,1)-1,mod(row()-2,5)*6+5,1,6)

In the row and column iterators, 5 is used because there are 5 columns for "record data".

Demo

Spreadsheet