Passing different arguments to function for each dataframe in a list

Here's a simplified example of my data:

I have a list of dataframes

set.seed(1)
data1 <- data.frame(A = sample(1:10))
data2 <- data.frame(A = sample(1:10))
data3 <- data.frame(A = sample(1:10))
data4 <- data.frame(A = sample(1:10))
list1 <- list(data1, data2, data3, data4)

And a dataframe containing the same number of values as there are dataframes in list1

data5 <- data.frame(B = c(10, 20, 30, 40))

I would like to create a new column C in each of the dataframes within list1 where:

C = A * (B/nrow(A))

with the value for B coming from data5, so that B = 10 for the first dataframe in list1 (i.e. data1), and B = 20 for the second dataframe data2 and so on.

From what I've read, mapply is probably the solution, but I'm struggling to work out how to specify a single value of B across all rows in each of the dataframes in list1.

Any suggestions would be hugely appreciated.