  We calculate an explicit lower bound on the proportion of elliptic curves
that are modular over any Galois CM field not containing $\zeta_5$. Applied to
imaginary quadratic fields, this proportion is at least $2/5$. Applied to
cyclotomic fields $\mathbb{Q}(\zeta_n)$ with $5\nmid n$, this proportion is at
least $1-\varepsilon$ with only finitely many exceptions of $n$, for any choice
of $\varepsilon > 0$.
