Below is an incomplete c# code snippet that may help with the conversion:

using System;
using System.Data;
using System.Linq;
using System.Security.Principal;


public class ConversionExample
{

    private string ConvertHexSidToStringSid(string hexSID)
    {
        // Check if hexSID has is prefixed with '0x'. Remove it if it does.
        if (hexSID.StartsWith("0x"))
            hexSID = hexSID.Substring(2);
        // Convert the hex string to a byte array.
        byte[] sidBytes = Enumerable.Range(0, hexSID.Length).
    Where(x => x % 2 == 0).
    Select(x => Convert.ToByte(hexSID.Substring(x, 2), 16))
    .ToArray();
        // Return the string SID
        return new SecurityIdentifier(sidBytes, 0).ToString();
    }
}

It converts from a hex string to a byte array, then uses the C# library System.Security.Principal to do the conversion from the byte array to the to the SID and casts it to a string.

I'm not aware of a way to do this without the C# library System.Security.Principal, but there were multiple posts online when I referenced this conversion, so there may be some options.

Had to convert SIDs for users as part of a conversion of a client from Windows Accounts to SAML accounts. Not C# versed, so I spent some time vetting out another solution. I wanted to do this in powershell, but ended up borrowing some vbscript code. 

Save this code to a file, i.e. "convertsids.vbs" and execute from a CMD prompt with the hexsid as the single parameter: 

cscript /nologo convertsids.publish.vbs 010500000000000515000000FF869BA35EB1DC6FAA3E7C2717FB0C00

output will be: hexSID, stringSID, i.e.: 

010500000000000515000000FF869BA35EB1DC6FAA3E7C2717FB0C00,S-1-5-21-2744878847-1876734302-662453930-850711

vbscript code

Dim Arg
Set Arg = WScript.Arguments
hexSID = Arg(0)
strSID = HexStrToSID(hexSID)
WScript.Echo hexSID & "," & strSID

Function HexStrToSID(strSid) 
'converts a raw SID hex string to the according SID string (SDDL)
    Dim i, data, offset
    ReDim data(Len(strSid)/2 - 1) 
    For i = 0 To UBound(data) 
        data(i) = CInt("&H" & Mid(strSid, 2*i + 1, 2)) 
    Next 
    HexStrToSID = "S-" & data(0) & "-" & Byte6ToLong(data(2), data(3), data(4), data(5), data(6), data(7))

    blockCount = data(1)
    For i = 0 To blockCount - 1
        offset = 8 + 4*i
        HexStrToSID = HexStrToSID & "-" & Byte4ToLong(data(offset+3), data(offset+2), data(offset+1), data(offset))
    Next
End Function 

Function OctetToHexStr(var_octet)
'converts pure binary data to a string with the according hexadecimal values
    OctetToHexStr = ""
    For n = 1 To lenb(var_octet)
        OctetToHexStr = OctetToHexStr & Right("0" & hex(ascb(midb(var_octet, n, 1))), 2)
    Next
End Function

Function Byte4ToLong(ByVal b1, ByVal b2, ByVal b3, ByVal b4)
'converts 4 bytes to the according lang integer value
    Byte4ToLong = b1
    Byte4ToLong = Byte4ToLong * 256 + b2
    Byte4ToLong = Byte4ToLong * 256 + b3
    Byte4ToLong = Byte4ToLong * 256 + b4
End Function


Function Byte6ToLong(ByVal b1, ByVal b2, ByVal b3, ByVal b4, ByVal b5, ByVal b6)
'converts 6 bytes to the according lang integer value
    Byte6ToLong = b1
    Byte6ToLong = Byte6ToLong * 256 + b2
    Byte6ToLong = Byte6ToLong * 256 + b3
    Byte6ToLong = Byte6ToLong * 256 + b4
    Byte6ToLong = Byte6ToLong * 256 + b5
    Byte6ToLong = Byte6ToLong * 256 + b6
End Function