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We present a study of the connection between the escape fraction ofLyman-alpha (Ly$\alpha$) and Lyman-continuum (LyC) photons within a sample ofN=152 star-forming galaxies selected from the VANDELS survey at$3.85<z_{spec}<4.95$. By combining measurements of H$\alpha$ equivalent width$(W_\lambda(\rm{H\alpha}))$ derived from broad-band photometry with Ly$\alpha$equivalent width $(W_\lambda(Ly\alpha))$ measurements from VANDELS spectra, weindividually estimate $f_{\rm{esc}}^{Ly\alpha}$ for our full sample. Inagreement with previous studies, we find a positive correlation between$W_\lambda(Ly\alpha)$ and $f_{\rm{esc}}^{Ly\alpha}$, increasing from$f_{\rm{esc}}^{Ly\alpha}\simeq0.04$ at $W_\lambda(Ly\alpha)=10$\r{A} to$f_{\rm{esc}}^{Ly\alpha}\simeq0.1$ at $W_\lambda(Ly\alpha)=25$\r{A}. For thefirst time at $z\sim4-5$, we investigate the relationship between$f_{\rm{esc}}^{Ly\alpha}$ and $f_{\rm{esc}}^{\rm{LyC}}$ using$f_{\rm{esc}}^{\rm{LyC}}$ estimates derived using the equivalent widths oflow-ionization, FUV absorption lines in composite VANDELS spectra. Our resultsindicate that $f_{\rm{esc}}^{\rm{LyC}}$ rises monotonically with$f_{\rm{esc}}^{Ly\alpha}$, following the relation$f_{\rm{esc}}^{\rm{LyC}}\simeq 0.15^{+0.06}_{-0.04}f_{\rm{esc}}^{Ly\alpha}$.Based on composite spectra of sub-samples with roughly constant$W_\lambda(Ly\alpha)$, but very different $f_{\rm{esc}}^{Ly\alpha}$, we showthat the $f_{\rm{esc}}^{\rm{LyC}}-f_{\rm{esc}}^{Ly\alpha}$ correlation is notdriven by a secondary correlation between $f_{\rm{esc}}^{Ly\alpha}$and$W_\lambda(Ly\alpha)$. The $f_{\rm{esc}}^{\rm{LyC}}-f_{\rm{esc}}^{Ly\alpha}$correlation is in good qualitative agreement with theoretical predictions andprovides further evidence that estimates of $f_{\rm{esc}}^{\rm{LyC}}$ withinthe Epoch of Reionization should be based on proxies sensitive to neutral gasdensity/geometry and dust attenuation.

Connecting the escape fraction of Lyman-alpha and Lyman-continuum photons in star-forming galaxies at $\mathbf{z\simeq 4-5}$