Yes, this is a valid Latin Square since each letter occur on ly once in each column and row.
\(y_{ijk}=\mu+\tau_i+\beta_j+\alpha_k+\epsilon_{ijk}\)
batch <- c(rep(1,5),rep(2,5),rep(3,5),rep(4,5),rep(5,5))
day <- c(seq(1,5),seq(1,5),seq(1,5),seq(1,5),seq(1,5))
value <- c(8,7,1,7,3,11,2,7,3,8,4,9,10,1,5,6,8,6,6,10,4,2,3,8,8)
ingre <- c('A','B','D','C','E','C','E','A','D','B','B','A','C','E','D','D','C','E','B','A','E','D','B','A','C')
dat <- data.frame(batch,day,value,ingre)
dat$batch <- as.factor(dat$batch)
dat$day <- as.factor(dat$day)
dat$ingre <- as.factor(dat$ingre)
aov.model <- aov(value~batch+day+ingre, data = dat)
summary(aov.model)## Df Sum Sq Mean Sq F value Pr(>F)
## batch 4 15.44 3.86 1.235 0.347618
## day 4 12.24 3.06 0.979 0.455014
## ingre 4 141.44 35.36 11.309 0.000488 ***
## Residuals 12 37.52 3.13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The ingredients appears to significantly affect the reaction time of the chemical process, since the p value is smaller than 0.001.