If you don’t include the letter ‘q’ when your are pronouncing cinq livres, French people can hear saint, like holy book.

When livre = book, the usual pronunciation always includes a brief ‘q’ even in front of a consonant to discriminate signification.

As you wrote later in your question, the cinq example is indeed a poor choice.

The reason is it is not pertaining to the list of words subject to liaison. A liaison happen when a word has an ending consonant only pronounced when the word is followed by a vowel or a mute h but not in other cases, like for example when the word is alone or the last one of a sentence.

On the opposite, cinq has its last consonant pronounced in that latter case and can actually always be pronounced. Sometimes, its last [k] is not pronounced when the following word starts with a consonant. This is an elision case, not a liaison one.

Back to your title question, no, words that are subject to liaison never have their last consonant causing an audible effect before a word starting with another consonant. These words are always pronounced just like if this letter does not exist at all. Doing otherwise it is a typical non native speaker mistake, like “Un petit garçon” pronounced like “Un petite garçon“.

Ok, Let’s not focus on this “cinq”. What you are talking about is liaison

If I’m not mistaken, the “liaison” only occurs with plural.
les enfants, les avions…
The following word begins with a voyel.

There is no liaison with proper nouns
Paris a de grandes rues (don’t pronounce the ‘s’)

There are some exceptions.

Les haricots (beans). As “haricots” begins with a consonant, there is no liaison. Same for “handicapés”.

But, I have always heard les hopitaux with the liaison.

Also, to complete the answer, Jilliagre is right, there is no “liaison” with words ending by a consonant.

Ok. If I understand well, you want to know which silent letters do which sound.
Let me first first recall you that there is three types of "liaisons" in french: the necessary ones, the optional ones and the forbidden ones. I’m saying that, because the liaisons that I’m presenting are sometimes optional.
There is in french 6 liaisons’ sounds.

• /z/, which is done with a final "s", "z" or "x".
• /t/, which is done with a final "t" or "d"
• /n/, which is done with a final "n"
• /p/ (always optional) which is done with a final "p"
• /r/ ( always optional) which is done with a final "r"
• /k/ (always optional) which is done with a final "c" or "g"

Several remarks:

• the three last liaisons are really rare.
• the "r"-liaisons is said to be necessary with the adjectives "premier" and "dernier" by the Académie français. I’m not here to say what I think about the Académie française, but you have to know that what they say is always interessing, but often not representative to what the french speakers say and write.
• For the number between 1 and 10, it’s really some crap. Here is the list explaining for each of them:
• un (liaison in /n/)
• deux (liaison in /z/)
• trois (liaison in /z/)
• quatre (nothing)
• cinq (crap! It depends on regions. In some regions, the "q" is always pronounced. In the other, like mine, it is only pronouced if the next word begins with a vowel (like a liaison) but also if it is followed by a break (point or comma).
• six (crap! Almost like cinq. It is pronouced /z/ before a vowel-begining word and !!! /s/ before a break. )
• sept (the "t" is always pronounced)
• huit (crap! exactly like cinq, but with the sound /t/ instead of /k/)
• neuf (crap! Almost like six. It is pronouced /v/ before a vowel-begining word and !!! /f/ before a break. )
• dix (crap! Exactly like six)

I hope I have answered your question. There is still a lot of things to say about the liaisons. So feel free to ask if you have other questions 🙂

By the way if there is an answer satisfying you, please mark it in order to show that the topic was … answered!