Carbaldehyde or formyl?
The name ‘5-methylbenzyl-3-carbaldehyde-1-oic acid’ is not correct for several reasons. In the following, I focus on the question in the title concerning the choice of ‘carbaldehyde’ or ‘formyl’.

Both, ‘carbaldehyde’ and ‘formyl’, denote the substituent group $\ce{-CHO}$ and can be used, among other ways, to systematically name some aldehydes.

The part ‘carbaldehyde’ is a suffix. It can be used when the $\ce{-CHO}$ group is attached to a ring, for example cyclohexanecarbaldehyde. However, the preferred IUPAC name (PIN) for the analogous benzene derivative is ‘benzaldehyde’, which is derived from the retained name of the corresponding carboxylic acid.

The part ‘formyl’ is a prefix. It can be used in the presence of a characteristic group having priority to be cited as a suffix or when the $\ce{-CHO}$ group is attached to a side chain.

The compound given in the question contains two characteristic groups, $\ce{-CHO}$ and $\ce{-COOH}$. The principal characteristic group must be expressed at the end of a name by means of a suffix or a class name, or implied by a trivial name. Since $\ce{-COOH}$ is the senior characteristic group in this case, the compound is named ‘3-formyl-5-methylbenzoic acid’ (not ‘3-carboxy-5-methylbenzaldehyde’). Note that the $\ce{-CHO}$ group cannot be expressed at the end of a name; it has to be expressed as a suffix (i.e. ‘formyl’).