First of all it's not an "equation", for to be
called an equation, there must be an equal
sign in it.  Otherwise it is called "an expression"

Equations are said to be "solved"
Expressions are said to be "simplified".

So much for correct wordage.  Let's look at what
you did:

That is wrong

You thought the 5+w-3w became 2w, but it doesn't.

Let's look at 

5+w-3w

You must combine only like terms. the term "5" and
the term "-3w" are NOT like terms.  so you cannot
combine them as you tried to do and got "2w".  You also
cannot ignore the "w" sitting there in between them    

That "w" means "1w", so let's write it that way:

5+1w-3w

The only like terms are the "1w" and the "-3w".  You 
combine them by combining their coefficients 1-3 as
-2 and then putting the letter "w" on, getting "-2w".

So 

5+1w-3w

becomes 

5-2w,  not "2w"

So starting over your corrected simplification is:

w+3w+4(5+w-3w)

Put in the invisible 1 coefficients on the "w"'s

1w+3w+4(5+1w-3w)

Combine the terms of "1w+3w" as "4w"
Combine the terms of "1w-3w" as "-2w"

4w+4(5-2w)

Use the distributive principle to multiply
the 4 just before the parentheses by both terms
inside the parentheses.  You get:

4w+20-8w

Now combine the "4w" term with the "-8w" term
and get "-4w"

-4w+20

That's the final simplification.

Edwin