Catalyzes the transfer of a phosphate group to glutamate to form L-glutamate 5-phosphate (PubMed:29777624). May be important for growth and survival (PubMed:29777624). ATP + L-glutamate = ADP + L-glutamyl 5-phosphate Inhibited by L-proline as part of a negative feedback loop. Also inhibited by L-proline analogs 3,4-dehydro-L-proline, L-azetidine-2-carboxylic acid and L-4-thiazolidine carboxylic acid. Amino-acid biosynthesis; L-proline biosynthesis; L-glutamate 5-semialdehyde from L-glutamate: step 1/2. Homotetramer; oligomerization is not affected by L-proline feedback inhibition. Expressed in promastigotes. Belongs to the glutamate 5-kinase family.