Question

5 = 500e^-0.00043(t)

Answer 1

T = (e^0.00043)/100) in its exact form
or
t = 0.0100043 in decimal form.

Some simple math.
First, let’s get rid of easily divisible numbers.

5 = 500 * e^(-0.00043) * t

Let’s divide both sides by 5 so we can have one on the left side of the equation, where anything multiplied would stay the same value.

5/5 = 500/5 * e^(-0.00043) * t
1 = 100 * e^(-0.00043) * t

As for Euler's number, the exponent is negative, and numbers to a negative power over one is the same as one over the absolute value of the exponent.

1 = 100 * e^(-0.00043) * t
1 = 100 * 1/e^(0.00043) * t

We can multiply 100/1 with 1/e^(0.00043) to simplify.

1 = 100 * 1/e^(0.00043) * t
1 = 100/e^(0.00043) * t

Divide t on both sides.

1 = 100/e^(0.00043) * t
1/t = 100/e^(0.00043) * t/t
1/t = 100/e^(0.00043)

With any fractions the equal the same, flipping one means you just have to flip the other. If the ratios are equal, nothing will happen to the validity of their equivalence.

1/t = 100/e^(0.00043)
t/1 = (e^0.00043)/100
t = (e^0.00043)/100)

So, you have your answer in the simplest form. If you want to go the step further, you can get decimal form too. Just multiply the exponent and divide to get

t = 0.0100043

Answer 2

t=10709.69810694

Hope this helps! :)