how to make vim syn regex to capture word with trailing space?

I'm trying to make a vim regex to highlight word house in this example but only if followed by whitespace and only if sentence ends in semicolon.

herbert house mouse; bear care; house moose hat; // both instances of house highlighted
cow (house) banana goat; car bar; //house must NOT be highlighted
house beagle //house must NOT be highlighted

From my VIM syntax file:

syn match ngzRewLine '\w\+[^;]\{-};' contains=ngzRew
syn keyword ngzRew house contained

This works great except (house) is being highlighted. What regex can I use that will only match words with trailing whitespace and a non greedy ending semicolon?

EDIT

To summarise, words in the ngzRew keyword group should be highlighted in the following cases:

house mouse;
cat house mouse;
house banana;catfish house shoes;
house;

No highlight should appear in the following:

house
cat (house) cheese;

house is used here as an example but there are other keywords in the ngzRew keyword group and the behavior should be the same.

Solution

You could do it this way (this is probably not very convenient but I can't think of a better way because of the following whitespace)

highlight MyGroup ctermbg=green guibg=green
syntax match MyGroup /\(house\|car\)\ze\(;\|\s.\{-};\)/

Now it matches a car as well.

\ze matches at any position, and sets the end of the match there,
\s whitespace character,
. matches any single character,
\{-} matches 0 or more of the preceding atom, as few as possible,
\(\) braces can be used to make a pattern into an atom,
\| is "or" operator in a pattern.