Buy a first or second gen MR2 and put your 1MZ in it. That will be pretty quick. You can use the 5 speed too if you modify the shift shaft.
You can run a 3MZ exhaust cam and 2MZ intake cam in your 1MZ and that will add a bit of power. So would the supercharger kit others have mentioned.
One could build a turbo setup for possibly less, that would work better, but if you have never done that before it's going to get expensive fast. If you aren't doing the work yourself it's out of your budget. (Hint: 11psi on a pair of stock wrx td04l-13t turbos, 440cc injectors, walbro 190, speeduino or megasquirt, custom manifolds and intercooler. the oil gallery has two m18 plugs near the oil pump that can be removed and replaced with -an adapters to supply oil to the turbos, no idea if this would fit in a camry engine bay)
To be honest though, if 5k is out of your budget you don't really have enough to be building hot rods. Some days during a project like this it feels like you are lighting 100's and tossing them out the window.