To get past Lv. 5, you must beat the game once and then go into Challenge Mode.
In Challenge mode you will find "Mega" versions of your Lv. 5 weapons (you will not unlock the Mega version of a weapon unless it has reached Lv. 5).
You would want to buy these weapons as soon as you can because your old weapons are no match for the enemies you face in challenge mode.
These Mega weapons can be upgraded to a further two levels - Lv.5 > Mega > Giga > Omega.
Omega is the final weapon Lv you can upgrade it to.
After upgrading all your Weapons to their fullest (Omega for all weapons and Lv. 5 RY3NO - Rynocerator) you get the 'Omega Arsenal' trophy.