It is important to remember that in Algebra, whatever you do to one side of the '=', you must do the other side. For example, if you have:

5 + 5 = 6 + 4

If you subtract the 5 from the left hand side, you must do the same to the right hand side of the equal side for the equation to remain equal, like this...

5 + 5 -5 = 6 + 4 -5

Becomes...

10 - 5 = 10 - 5

This then becomes...

5 = 5

So with that in mind...

You start out with your equation written as:

-8(t + (-8)) - (t + 5) = 5

Multiply the number outside the parentheses to the terms in the parentheses to get this...

-8 times t = -8t ---> -8 times -8 = +64

for the next part, you have a negative sign (-) on the outside of the parentheses. That is the same as saying -1, but because it is one, we don't write it. So it is just a negative sign. The number 1 multiplied by anything results in the number you are multiplying by. If you multiply 1 times 8, the result is 8. 1 times 5 is 5, etc.
Now to continue...

-1 times t = -t ---> -1 times 5 = -5

So here is what we have so far...

-8t + 64 - t - 5 = 5

Now we combine like terms by adding or subtracting all terms with letters and then adding or subtracting all terms without letters like this...

-8t - t + 64 - 5 = 5

Because 8t and t are both negative, it is the same as saying -(8t + t), perform operation inside parenthesis first to get -(9t), and then remove the paren... Now subtract 64 - 5 = 59

-9t + 59 = 5

Now we want to move all like terms to the same side of the = sign. We do it like this...

-9t +59 -59 = 5 - 59

Subtracting 59 from both sides, you get 0 on the left side and -54 on the right side of the equal, like this...

-9t = -54 we can make this easier by multiplying -1 on both sides to change the signs to + like this...

-1(-9t) = -1(-54) that gives you ---> 9t = 54

Now divide both sides by nine to complete moving like terms to the same side...

9t/9 = 54/9 this gives you the answer ---> t = 6

We can check out work by getting the original equation and substituting the 6 in place of t.

-8(6 + -8) - (6 + 5) = 5 ---> -48 +64 - 6 - 5 = 5 ---> 5 = 5

It works, so your answer is t = 6.

-8(t+-8)-(t+5)=5

*You have to multiply the -8 by what's inside of the parenthesis.*

-8xt= {-8t}, -8x-8={64},  (-)xt={-t}, (-)x5={-5}

-8t+64-t-5=5

*Now you must combine like terms*

-8t-t= -9t

64-5=59

-9t+59=5

*Now you must subtract 59 from both sides to get (-9t) by itself.*

59-59=0 *therefore it cancels out*, 5-59= -54

-9t=-54

*Now that you have -9t by itself you can divide both sides by -9*

-9/-9= 1, -54/-9= 6

{t=6} - Final answer

Check the solution:

-8(6+-8)-(6+5)=5

-8x-2={16} - {11}= [5-Answer checked.]