When do I use the d 5 gear in acura 2003 tl 3.2 liter

Pretty much all the time!

D3, D4, and D5 are all just *DRIVE* like on any automatic transmission, EXCEPT
that the number next to the D is the "highest gear the automatic transmission will go into".
The Acura just gives you a choice, in case you don't want to go into a higher gear (like if it's slippery traction or a steep hill, etc.)

1 means: Manual gear. FIRST GEAR ONLY.
2 means: Manual gear. SECOND GEAR ONLY.
D3 means: Use automatic transmission, but engine will never shift above 3rd gear.
D4 means: Use automatic transmission, but engine will never shift above 4th gear.
D5 means: Use automatic transmission, but engine will never shift above 5th gear.