It may be useful to distinguish between "repeats" and "replicates" in this case. The terminology is definitely not standardized, though.
In this case, your description might be interpreted as a single study with five "repeats". That is, the five experiments were all conducted during the same two weeks, perhaps on the same lab bench. No experimental intervention was performed (for example, dosing the cells with some chemical, or changing the type of media, or varying the temperature, etc.). In this case, there is not much to be done other than to calculate the variation (e.g., by using the sample standard deviation). The sources of variability here are probably primarily biological.
Or, your description might be interpreted as a set of serial studies, with each study taking two weeks. In each study, you may or may not have had multiple repeat experiments. I would call this situation "replicates" in this case, because you have replicated the entire study. It would be reasonable to call these "blocks", also.
If you only had one repeat in each replicate, then it is more or less the same situation as before --- simply calculate the sample standard deviation. However, in addition to the biological variability, the variability now includes anything else that may have changed across the replicates, including both "random" variation and any systematic effects happening over time.
If you had more than one repeat per replicate, then you can think in terms of partitioning the variance between repeats and replicates. This is the situation in which the one-way analysis of variance would be useful, though you would probably wish to think of replicates as a random effect rather than as a "fixed" effect. This has gone under the name of variance components analysis in the past. Here, the two components would be repeat-to-repeat variance (presumably mostly biological and assay related) and replicate-to-replicate variance (presumably relating to experimental set-up or any other time effects).
To be honest, though, this is all probably not of major interest to you. Most likely what you will be doing down the road is applying experimental treatments of some sort, such as varying the media, varying the cell types, or doing things to the cells. You will then want to know the effects of these experimental treatments upon antibody production and cell growth.
But, at that point, you will be able to use the data from these preliminary experiments to decide how to structure your studies. The choices you will have to make are things like: How many repeats should you allocate per experimental treatment? How many replicates should I perform?