Avoid repeating letters between five simple programs

CJam, 73 bytes

"Obkkh+'Phukc&"7f^
q~m!
ri){'j3+_3++~},:+
lS-el_&
4{_' *4@-Y*('**+}%_1>W%\+N*

Each line is a full program. Try them online: 1 | 2 | 3 | 4 | 5

Letter map

 bc  f h  k   op    u       18
            m   q            4
        ij       r          17
    e      l      s          7
             n        w y   27

If you want (and each of your programs fits in a line), you can use this CJam program to create a letter map for your own submission.

Pyth, 90 bytes

First attempt...

Task 1: 20 bytes

+"Hello, "+C87"orld!

Task 2, 3 bytes

.!Q

Task 3, 9 bytes

sf}TPTSvz

Task 4, 6+8=14 bytes

@G{rw0

Task 5, 44 bytes

"   *
  ***
 *****
*******
 *****
  ***
   *

osascript, 759 Bytes

I knew this was going to be a lot when I started. o-o

Task 1: 15 Bytes

"Hello, World!"

I knew that it was going to be bad from this point.

Task 2: 64 + 8*4 = 96 Bytes

on run a
set o to 1
repeat a
set o to a*o
set a to a-1
end
o
end

Oh gawd.

Task 3: 170 + 8*13 = 274 Bytes

on run a
set o to 0
set t to false
repeat with i from 2 to a
set t to true
repeat with c from 2 to i-1
if i mod c=0 then set t to false
end
if t then set o to o+i
end
end

Dennis ≠ outgolfed.

Task 4: 225 + 8*13 = 329

on run a
set o to""
repeat with i in items of a
repeat with c in characters of i
if c is not in o then
if ASCII number of c<91 then
set o to o&(ASCII character of(ASCII number of c+32))
else
set o to o&c
end
end
end
end
o
end

...

Task 5: 45 Bytes

"   *
  ***
 *****
*******
 *****
  ***
   *"

So, yeah. I knew I was gonna lose from the start. But it was interesting, I'd be interested to know if there's a way to do this in fewer characters. Character map (as provided by Dennis):

   de  h   l  o  r    w     15
a cdef hi  lmnop rstu w    160
a  de        nop rstu       57
abcdef hi  lmnop rstu w    214
                            39
                             0

The character count above is slightly off - newlines made it have issues, as the newlines were uncounted.

NOTE: The reason for not using stuff like a's characters or the like is that the ' character has to be used when executing from the osascript command line. If I had used ', I'd have to use \' or something similar, which wouldn't have helped me at all. Also, it only recognizes " as string capturers, so I was kinda screwed there as well. But that was fun.