The question now becomes: is there a way to set the on/off periods individually for each of the 5 LEDs?
Yes, but you have to create the individual ON/OFF periods.
That code only has 1 period, for a 50% dutycycle.

So many things you can do.
So little time to explain.
Twinkle Twinkle little tree ...
Code:
DEFINE OSC 4
DEFINE BLINKYFREQ 100  ; 10mS periods

' ***************************************************************
' Device Fuses
' ***************************************************************
#CONFIG
   __config _CONFIG1, _FOSC_INTOSC & _WDTE_ON & _PWRTE_ON & _MCLRE_OFF & _CP_OFF & _CPD_OFF
   __config _CONFIG2, _PLLEN_OFF & _STVREN_ON & _BORV_LO & _LVP_OFF
#ENDCONFIG

OSCCON   = %01101000        ' 4MHz internal osc

;----------------------------------------------------------------
LEDcount    CON 5                  ; Number of LEDs on the PORT
OnTimes     DATA  50,22,38,75, 5   ; default periods for each Output
OffTimes    DATA 150,45,38,95,34

;----------------------------------------------------------------
#DEFINE USE_RANDOM_SEQUENCE     ; comment for contiuous Sequence
#IFDEF USE_RANDOM_SEQUENCE
    RND     VAR WORD : RND = 13864
    MIN_ON  CON 10                  ; Minimum random ON time
    MAX_ON  CON 100                 ; Maximum random ON time
    MIN_OFF CON 10                  ; Minimum random OFF time
    MAX_OFF CON 100                 ; Maximum random OFF time
    RandPeriod VAR WORD[LEDcount]
    RandPeriods DATA WORD 1000, WORD 1250, WORD 1500, WORD 1750, WORD 2000
#ENDIF

;----------------------------------------------------------------
CCPR1val   CON EXT      : @CCPR1val = (OSC*1000000/4)/ BLINKYFREQ
CCPR1      VAR WORD EXT : @CCPR1 = CCPR1L
Timer1     VAR WORD EXT : @Timer1 = TMR1L
CCPIF      VAR PIR1.2

LoopLED    VAR BYTE[LEDcount]
OnTime     VAR BYTE[LEDcount]
OffTime    VAR BYTE[LEDcount]
x          VAR BYTE

;----[Initialize]------------------------------------------------
FOR x = 0 to LEDcount - 1         ; load the periods from EEPROM
    READ OnTimes+x, OnTime(x)
    READ OffTimes+x, OffTime(x)
    #IFDEF USE_RANDOM_SEQUENCE
        READ RandPeriods+(x<<1), WORD RandPeriod(x)
    #ENDIF
NEXT X

;-- setup CCP1 and Start Timer1 --
CCPR1   = CCPR1val     ; set compare value
CCP1CON = %00001011    ; compare mode, special event 
Timer1  = 0            ; clear Timer1
T1CON.0 = 1            ; start Timer1

ANSELC = 0
TRISC = 0              ; PORTC all OUTPUT

;----[Main Program Loop]----------------------------------------
Main: 
    x = (x + 1) // LEDcount
    PORTC.0(x) = !!(LoopLED(x) < OnTime(x))
    LoopLED(x) = (LoopLED(x) + 1) // (OnTime(x) + OffTime(x))
    #IFDEF USE_RANDOM_SEQUENCE
        RandPeriod(x) = RandPeriod(x) - 1
        IF RandPeriod(x) = 0 THEN
            READ RandPeriods+(x<<1), WORD RandPeriod(x)
            RANDOM RND
            OnTime(x) = (MAX_ON - MIN_ON)* RND.HighByte / 255 + MIN_ON 
            OffTime(x)= (MAX_OFF - MIN_OFF)* RND.LowByte / 255 + MIN_OFF
        ENDIF
    #ENDIF
    IF x != (LEDcount - 1) THEN Main

Waiting: IF !CCPIF THEN Waiting
    CCPIF = 0
GOTO Main