Please mention the sensor of Landsat 5, is it MSS or TM? Assuming it is Thematic Mapper data, you have visible red and shortwave infrared data. You can directly infer from the band reflectance values about where vegetation patches lie and hence moisture content.
Band 3 (Red) can help you discriminate vegetation slopes and Band 5 (SWIR) can help you discriminate moisture content of soil and vegetation. You can calculate band ratios or normalized band indices to ascertain drought stress or soil moisture.
You can calculate Normalized Difference Water Index (NDWI) or Normalized Difference Soil Index (NDSI) and Normalized Difference Vegetation Index (NDVI).
For Landsat TM, NDWI = (Band 3 - Band 5)/ (Band 3 + Band 5). This is the only index you can calculate with the data available to you. If you have access to Band 4 (NIR), you can additionally compute Soil index,NDVI,NVMI and Soil adjusted vegetation index (SAVI). Hope this helps.