Acidity of phenol and carboxylic acid
Since you haven't mentioned the carboxylic acid to be measured, I assume the carboxylic acid to be $\ce{HCOOH}$. It has a $\mathrm pK_\mathrm a$ of $3.75$
Now, as you mentioned, phenol (or carbolic acid) has a $\mathrm pK_\mathrm a$ of $10.0$. There is a difference of about $6$ in the two values. This is because of the effective delocalization that takes place in formic acid compared to that of phenol. The best way to check for this is by computing the charges on the atoms in their respective conjugate bases and then check the stabilities of the two.
So first, we check the delocalization on the phenoxide ion.
The Mulliken partial charges on the atoms ($\ce{C-1}$ as carbon connecting to oxygen and we move counter-clockwise. $\ce{H-2}$ signifies the hydrogen bonded to $\ce{C-2}$)
$$ 
\begin{array} {c}
\begin{array}{lr}
\text{Atom} &amp; \text{Charge} \\ \hline
\ce{C-1} &amp; 0.307 \\
\ce{C-2} &amp; -0.246 \\
\ce{C-3} &amp; -0.204 \\
\ce{C-4} &amp; -0.243 \\
\ce{C-5} &amp; -0.204\\
\ce{C-6} &amp; -0.246 \\
\end{array}
\begin{array}{lr}
\text{Atom} &amp; \text{Charge} \\ \hline
\ce{H-1} &amp; 0.103 \\
\ce{H-2} &amp; 0.100 \\
\ce{H-3} &amp; 0.089 \\
\ce{H-4} &amp; 0.100 \\
\ce{H-5} &amp; 0.103\\
\ce{O} &amp; -0.659\\
\end{array}
\end{array} 
$$
Now, we check the delocalization on the formate ion,
$$
\begin{array}{lr}
\text{Atom} &amp; \text{Charge} \\ \hline
\ce{C} &amp; 0.363 \\
\ce{H} &amp; -0.083 \\
\ce{O-1} &amp; -0.639 \\
\ce{O-2} &amp; -0.639 \\
\end{array}
$$
Comparing the two, we can see that the more effective delocalization has taken place in formic acid since the net charge on an individual oxygen atom is less ($-0.659$ in phenoxide ion and $-0.639$ in the formate ion)
Due to this, we can say that the net effective charge is much better delocalized in formic acid which means that the conjugate base is better stabilized. Even though there were five possible resonance structures for the phenoxide ion, there do not contribute to the final resonance hybrid as well as the two equivalent resonance structures for the formate ion.
Since order of conjugate base stability is directly proportional to acidity. Hence formic acid would be more acidic than phenol.
Note: These values were calculated on WebMO with geometry optimization using Gamess DFT B3LYP/3-21G