Currently have one card (3k CL). Possible to get a 5k CL Visa Signature anywhere?

[Anonymous]

So I am looking to get a new card.  Preferably a Visa Signiture for the travel benefits, >=1.5% cash/points back, and preferrably no annual fee. 

I started with a Capital One student journey card about 4 years ago.  $300 CL grew to $900 and stopped.  Called the EO last year and they upped to $1,500/Quicksilver 1.5% Cash.  It just upgraded to $3,000.

Are there any cards/banks I should look in to in effort to possibly get the $5,000CL needed for the Visa Sig?  Is it an unlikely scenario?

[Anonymous]

Try the venture or the chase sapphire

[B335is]

What does your credit reports look like? Anything negative? An existing line with $5k would really be helpful but not impossible. Have you checked any of the pre approvals? Some Cap1 customers have seen some pretty high limits on Venture lately.

[Anonymous]

Im around 750 with almost 4 years of history.  Just one card and one auto loan with nothing bad/everything paid on time.