confused re ppi and large print resolution
1589x1181 and divide that by 16x20 (320) i arrive at 5864 and if i get the square root of this I get only 76 pixels per inch, which is about half of the minimum 150 ppi which I have seen on these forums.
1589 x 1181 pixels isn’t a 4:5 (16:20) aspect ratio, so you would have to crop the image slightly to 1476 x 1181 for it to fit that ratio. The height would work out at about 74 ppi (actually 73.8125), and the width, when trimmed, would be the same.
If you want to see how it will look after printing, crop it to 4:5 and then have a print made from a section of it. You could take a 1/4 of it and have an 8 x 10 inch print made, or a 1/16 of it and have a 4 x 5 inch print made.
There is nothing magic about 300 ppi. The figure comes from offset printing at 150 lpi (lines per inch), where it was thought that approximately twice the image resolution would lead to a good final print resolution. Most Epson printers, for example, use an RGB input resolution of 360 ppi to form a final CMYK print at 1440 or 2880 dpi.
I don’t know what up-sizing algorithms Elements has, but you could try up-rezing it to 240-360 ppi at 16 x 20 inches, preferably using a bicubic algorithm. Then view it on the screen at 100%, and see if that looks resolved enough for you. You will probably have to resharpen it a little after up-rezing.
If you want to see whether you should up-rez or let the printer do it, then you could have two 4x 5 prints made, one before up-rezing and one after.