Suzuki ls400 wil not accelerate and backfires

Try checking for a bent rim.

Typically this has to do with timing, check the timing

Hi and welcome to fixya,

You change gear ratios if you wanna increase the top speed on a C50. A smaller gear on the rear will give allow to go faster but will sacrifice on power and acceleration. It also means that you indeed go faster from 150 kph max to 170 to 200 kph. That's a big leap and it will take you more time to achieve the speed. If you drive mostly on flat roads, it shouldn't be a problem. But if you go uphill and tend to prioritize dragging power (for stop and go applications), i would still recommend not changing the gear ratios.

Meanwhile, you may increase its performance by purchasing a stage 1 dyno kit and a performance exhaust. These exhaust are more open and will let exhaust fumes out. It could give around +15 HP kick with the proper exhaust. I would also recommend changing the plugs to iridium and change oil filter and air filter to K&N high-flo filters. This will guarantee a performance upgrade on your bike and result is faster acceleration and quicker to reach top speed.

Hope this helps.
Let me know if you want more info so i could detail.

Sounds like this bike sat for a while.

When bikes sit, the jets and the needles that go through them corrode both contributing to leaning the mixture.

Replace the jets, replace the metering needles, and while you're in there, replace the float valves and their seats.

SOUND LIKE THE FUEL PUMP.ITS TOO WEAK.NOT SUPPLYING ENOUGH FUEL WHEN DRIVING FASTER SPEED.

Backfiring is typical for 'lean' conditions and stuck inlet valves.
check also the spark plug condition, replace them if any doubt on their age exists.
Check compression to discover open valves.
Clean out the carburettors.