Where is the fuel pump relay on a 2005 Toyota solara

More information please. What EXACTLY does it do when you turn the Key? Are there any other lights on the dash that aren't normally there? A slow or lazy cranking over is commonly a flat or old battery. Batteries used for over 5 years are considered 'Old'.
Cranking but not trying to start is likely to be a spark problem. Cranking, trying and stalling out is normally a fuel issue. Nothing at all is often a fuse or relay issue.

It is more than likely the fuel pump. Sometimes you can bang a bit on the bottom of the fuel tank to get one to start for a minute or more. You can also listen to the fuel pump running by opening the fuel cap and listening there, while having someone turn on the ignition switch. You should hear a hum for a few seconds each time the Ign. is switched off & on.

There is probably an inertia type fuel cut off though in the early days of fuel injection a relay was used incorporating electronics monitoring the current drawn by the fuel pump. If a fuel line ruptured the current would fall and the relay would cut off the power to the pump.

The inertia type switch was sometimes sited in the rear luggage space and sometimes in the engine compartment but often behind a footwell kick panel.

If you are going to bypass the fuel safety system it should be replaced by a manual switch and a deadman system - the amount of fuel an unfettered healthy pump can shift is many litres per minute with a huge potential for fire in the case of a collision.

You have to inspect the fuel pump again if the fuel pump ok there is a short circuit between the relay to fuel pump the most you have to inspect is the wire inside the tank

No, the timing belt does no run the water pump

The fuel filter on a 2002 Camry is an "In-Tank Filter". This means the filter is in the gas tank and is integrated with the fuel pump. In order to replace the filter, you must remove the tank and disassemble the fuel pump.
Toyota's service schedule, which can be found at ToyotaOwnersOnline.com, does not list the fuel filter replacement through 120K miles (as high a the schedule goes).
Thank you for using Fixya and hope this helps.

heres adiagram check the circled fuses, the fuse/relay box is located under the hood.

replace the fuel filter, if that does not work, check your fuel pump.

maybe a relay?check under hood and in cab!!!Good Luck!!!

Yes, it could be the fuel pump. The cheapest way to fully diagnose the problem is to get to a garage and have them hook it up to a OB2 port machine and have them pull the code. That code will tell exactly what is going on. More than likley you will have to go to a garage to get this fixed if it isn't easily fixed. Could also be the fuel rail on the motor(injectors). Good luck.