I ran the following code correctly:

#just.raw.counts was my countData and meta.data is my colData

>just.raw.counts = read.delim("Raw_counts_input.txt")
>just.raw.counts = read.delim("Raw_counts_input.txt", row.names=1)
>just.raw.counts <- as.matrix(just.raw.counts)
>meta.data = read.delim(file="meta_data.txt", row.names = 1)
>count.data.set <- DESeqDataSetFromMatrix(countData=just.raw.counts, 
                                         colData=meta.data, design= ~ condition) 
>count.data.set.object <- DESeq(count.data.set)

I had no issues to this point

Then I want to apply the apeglm shrinkage but first I ran this code below

>resultsNames(count.data.set.object)

and it gave me the coef below

[1] "Intercept"                 "condition_Day1_vs_Control" "condition_Day2_vs_Control" "condition_Day3_vs_Control"
[5] "condition_Day5_vs_Control"

Afterwards I ran the following code to perform the apeglm shrinkage:

count.data.set.object.2 <- lfcShrink(dds=count.data.set.object, coef=5, type="apeglm")

At this point there was not problem

Then I ran another code to show the result

res <- results(count.data.set.object.2, contrast=c("condition","Day1","Control"))

At this point, I got an error which is

Error in results(count.data.set.object.2, contrast = c("condition", "Day1",  : 
  is(object, "DESeqDataSet") is not TRUE

AT this point am dumbfounded and I don't know what to do.

Please help me

It's exactly what the error says. count.data.set.object.2 is not a DESeq object. It's a DESeqResults object.

Apologies to ask, but, did you check how this is done in the vignette? - see http://bioconductor.org/packages/devel/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#quick-start

You just seem to be running 2 commands in the incorrect order and have variables / coefficients in the incorrect place.

You could try something like:

just.raw.counts = read.delim("Raw_counts_input.txt")
just.raw.counts <- as.matrix(just.raw.counts)
meta.data = read.delim(file="meta_data.txt", row.names = 1)
count.data.set <- DESeqDataSetFromMatrix(
  countData=just.raw.counts, 
  colData=meta.data,
  design= ~ condition)
count.data.set.object <- DESeq(count.data.set)

# Day 5 versus control
res <- results(count.data.set.object, name = 'condition_Day5_vs_Control')
res <- lfcShrink(count.data.set.object, coef = 'condition_Day5_vs_Control', type = 'apeglm')

For other type of comparisons involving coefficients not listed by resultsNames(), take a look here: https://www.biostars.org/p/325009/#325036

Kevin