Unable to boot my Nexus 5 into recovery mode
The problem is your not flashing SuperSU or deleting /system/bin/install-recovery.sh. Android has safeguards which revert to the stock recovery thru the install-recovery.sh, SuperSU by default disables this function so I'd recommend flashing it after you install TWRP.

Steps


fastboot flash recovery twrp.img or fastboot boot twrp.img
flash twrp.img inside of recovery if you just booted it instead of using fastboot flash
flash SuperSU-2.79-SR3.zip


OR


tap the mount tab
tap System 
go back to main screen and tap advanced then file manager
navigate to /system/bin and delete install-recovery.sh


I recommend using the SuperSU route but whatever floats your boat.