You mean Earth Explorer right? https://earthexplorer.usgs.gov/
I tested it and I can find both Landsat 5 and 7 images in 1999 over Kathmandu. Did you make sure to select the correct satellites in the Data Sets tab?
You can obtain Landsat images of Kathmandu before 2000 from the USGS EarthExplorer website, which is the official archive for Landsat data. Here are the steps to follow:
Go to the EarthExplorer website: https://earthexplorer.usgs.gov/
Create an account or log in if you already have an account.
Click on "Search Criteria" and select "Landsat Archive" under the "Data Sets" tab.
Choose the time range for which you want to obtain Landsat imagery.
Enter "Kathmandu" in the "Place Name" field or specify the latitude and longitude coordinates for the area of interest.
Click on "Search" to view the available Landsat images for your selected area and time range.
Use the filters to narrow down your search based on sensor type, cloud cover, and other criteria as needed.
Once you have identified the Landsat image(s) you want to download, click on the "Download Options" button and follow the prompts to download the data in the desired format.
Note that Landsat imagery before 2000 may not be freely available, and you may need to pay a fee for access to the data. Additionally, be aware that Landsat imagery from this time period may not have the same level of quality or resolution as more recent images.