What would cause this anomaly?

[Bruce]

See if this helps.

Add TRISB = %00000000 to the initialization section of your code to set RB pins up as outputs.

Change each HIGH or LOW PORTB.? to PORTB.? = 1 or 0.

Does it work as expected?

[NavMicroSystems]

I'm not sure if you have already done in a part of your code that has not been posted,

PortA 4:0 are analog inputs by default, set them to digital!

[peterdeco1]

I'm sorry I didn't post the complete code. I tried to shorten my post. At the top of my program I have:
OSCCON = $60 'set int osc to 4mhz
adcon1 = 7 ' set inputs to digital
@ DEVICE MCLR_OFF, INTRC_OSC, WDT_ON, LVP_OFF, BOD_OFF, PWRT_ON, PROTECT_ON
TRISA = %11111111
TRISB = %00000000

Again - the anomaly is ONLY when PORTA.5 is the LAST to close, the LED on PORTB.3 does NOT light. But the program DOES jump to "REWARD" and the MOSFETS will turn on, but PORTB.3 stays low. If you close the switch on PORTA.5 first or second, PORTB.3 goes high the way it's supposed to. Thank you.