For reference, the card text for both cards

Dengar pilot ability:

"Once per round after defending, if the attacker is inside your firing arc, you may perform an attack against that ship."

R5-P8:

"Once per round, after defending, you may roll 1 attack die. On a hit result, the attacker suffers 1 damage. On a critical hit result, you and the attacker each suffer 1 damage."

The question is, after Dengar is attacked, can he do both his ability and R5-P8's ability? I thought he could do both, as they are both triggered at the same time (after defending), so I could choose which order to resolve them. After I did my attack with dengar my opponent said I couldn't use R5-P8's ability, since the timing window had now shifted to after Dengar attacked.

You're correct. The two abilities have the same trigger, so you can choose to resolve them in any order--and resolving one certainly doesn't prevent you from resolving the other.

Theoretically, if you triggered R5-P8 first, your opponent wouldn't have been able to argue at all. Next time you defend, tell your opponent you're triggering R5-P8 AND Dengar before going any further, then you can choose the order of resolution.