You may consider a general linear model to model the effects and interactions of the variables (soil-parameters and amendment) on the response (Nitrate).

The conditional distribution of Nitrate is presumably not normal but rather right-skewed. I would therefore suggest to use log(Nitrate) as response variable, or to use a generalized linear model of the gamma-family.

You may find this useful:

http://www.unc.edu/courses/2006spring/ecol/145/001/docs/lectures.htm

http://www.unc.edu/courses/2010spring/ecol/562/001/docs/lectures.htm

http://www.unc.edu/courses/2010fall/ecol/563/001/docs/lectures.html

and

http://data.princeton.edu/wws509/notes/

and similar pages.

Since you have five type of soils with five levels of each other as well as amendment A with three levels only, you need to use irregular design of experiment. Because the number of levels are different. In this case you use either factorial design or more sophisticated design that is D-optimal design. Bu using design of experiment you will be able to analyze your data systematically through fitting your data by empirical model. It will also give you interaction effect between these factors on your output response. 

Hi Niguss,

First, it is necessary to know whether your trial is field or greenhouse experiment. If it is field experiment, the five different soil types can be considered as experimental sites. On the other hand if your trial is under greenhouse condition, the five soil types can be considered as experimental units as a single experiment, and compared each other after treating them with three levels of a soil amendment. That means, 5 soil types by 3 levels of amendment can be laid out in randomized complete block with 3 or 4 replicates. Then as mentioned above based on the data collected for soil parameters, a general linear model can be followed using an appropriate statistical software, such as SAS. In addition, principal component analysis can be used in order to compare the five soil types, based on the treatments. 

If you make clear the experimental factors and treatment combinations, experimental design you want to use, whether field or pot trial, soil and plant meters on which data to be collected, etc. more information can be given. For additional information please read this book.

Gomez and Gomez. 1984. Statistical procedures for agricultural research.