  This paper constructs tilting bundles obtained from full strong exceptional
collections of line bundles on all smooth $4$-dimensional toric Fano varieties.
The tilting bundles lead to a large class of explicit Calabi-Yau-$5$ algebras,
obtained as the corresponding rolled-up helix algebra. A database of the full
strong exceptional collections can be found in the package
QuiversToricVarieties for the computer algebra system Macaulay2.
