Phenotype-Genotype for multi-hybrid crosses
In my opinion, the easier way is dealing with each trait separately, as if it was a simple monohybrid cross, and writing down each result:


Aa x aa &rarr; $\frac{1}{2}$ Aa;
BB x BB &rarr; 1 BB;
Cc x cc &rarr; $\frac{1}{2}$ Cc;
dd x Dd &rarr; $\frac{1}{2}$ Dd;
Ee x Ee &rarr; $\frac{1}{4}$ EE;


Now, simply multiply all the results:

$\frac{1}{2} * 1 * \frac{1}{2} * \frac{1}{2} * \frac{1}{4}$ &rarr; $\frac{1}{32}$

I don't know about your country, but in my country of birth all secondary books have a chapter for monohybrid cross and another chapter for dihybrid cross. I don't like that, it creates a nonexistent separation and it makes (some) students memorize concepts. Linkage apart, I like to say to my students to do not mind about dihybrid, trihybrid, tetrahybrid etc crosses, just treat them as individual monohybrid crosses combined.