Verified answer

C2H5OH will have the higher viscosity, because of its hydrogen bonding. (The OH at the end of the formula tells you there is hydrogen bonding.) CH3OCH3 does not have hydrogen bonding; all the Hs are bonded to Cs only.

Viscosity is a function both of molecular size and intermolecular forces. It's important that we are comparing molecules of roughly the same size here, because if we were a comparing a long hydrocarbon chain without hydrogen bonding to a short chain with hydrogen bonding, it would be tricker to figure out.

You can read more here:

http://jchemed.chem.wisc.edu/jcesoft/cca/CCA2/MAIN...

Scroll down to "relative viscosities of liquids."