Is someone born 4-5 months before me considered to be my elder? Or are we the same age?

In an absolute strict sense yes they are older than you therefore the elder of the two of you.    But  if you mean 'elder' in the sense of having authority over you, then no.  In that sense your 'elders' are adults.  No one under 18 has the authority over you - unless an adult has given them that authority as in a baby sitter or student monitor.  Also in a social/community sense the 'elders' are usually the oldest generations.  The grandparents